Systems and methods for network-based biological assessment

ABSTRACT

Systems and methods are directed to computerized methods and one or more computer processors for quantifying the perturbation of a biological system in response to an agent. A set of treatment data corresponding to a response of a biological system to an agent and a set of control data are received. A computational causal network model represents the biological system and includes nodes representing biological entities, edges representing relationships between the biological entities, and direction values representing the expected direction of change between the control data and the treatment data. Activity measures are calculated and represent a difference between the treatment data and the control data, and weight values are calculated for the nodes. A score for the computational model is generated representative of the perturbation of the biological system to the agent and is based on the direction values, the weight values and the activity measures.

BACKGROUND

The human body is constantly perturbed by exposure to potentially harmful agents that can pose severe health risks in the long-term. Exposure to these agents can compromise the normal functioning of biological mechanisms internal to the human body. To understand and quantify the effect that these perturbations have on the human body, researchers study the mechanism by which biological systems respond to exposure to agents. Some groups have extensively utilized in vivo animal testing methods. However, animal testing methods are not always sufficient because there is doubt as to their reliability and relevance. Numerous differences exist in the physiology of different animals. Therefore, different species may respond differently to exposure to an agent. Accordingly, there is doubt as to whether responses obtained from animal testing may be extrapolated to human biology. Other methods include assessing risk through clinical studies of human volunteers. But these risk assessments are performed a posteriori and, because diseases may take decades to manifest, these assessments may not be sufficient to elucidate mechanisms that link harmful substances to disease. Yet other methods include in vitro experiments. Although, in vitro cell and tissue-based methods have received general acceptance as full or partial replacement methods for their animal-based counterparts, these methods have limited value. Because in vitro methods are focused on specific aspects of cells and tissues mechanisms; they do not always take into account the complex interactions that occur in the overall biological system.

In the last decade, high-throughput measurements of nucleic acid, protein and metabolite levels in conjunction with traditional dose-dependent efficacy and toxicity assays, have emerged as a means for elucidating mechanisms of action of many biological processes. Researchers have attempted to combine information from these disparate measurements with knowledge about biological pathways from the literature to assemble meaningful biological models. To this end, researchers have begun using mathematical and computational techniques that can mine large quantities of data, such as clustering and statistical methods, to identify possible biological mechanisms of action.

Previous work has also explored the importance of uncovering a characteristic signature of gene expression changes that results from one or more perturbations to a biological process, and the subsequent scoring of that signature's presence in additional data sets as a measure of that process's specific activity amplitude. Most work in this regard has involved identifying and scoring signatures that are correlated with a disease phenotype. These phenotype-derived signatures provide significant classification power, but lack a mechanistic or causal relationship between a single specific perturbation and the signature. Consequently, these signatures may represent multiple distinct unknown perturbations that, by often unknown mechanism(s), lead to, or result from, the same disease phenotype.

One challenge lies in understanding how the activities of various individual biological entities in a biological system enable the activation or suppression of different biological mechanisms. Because an individual entity, such as a gene, may be involved in multiple biological processes (e.g., inflammation and cell proliferation), measurement of the gene's activity is not sufficient to identify the underlying biological process that triggers the activity. None of the current techniques have been applied to identify the underlying mechanisms responsible for the activity of biological entities on a micro-scale, nor provide a quantitative assessment of the activation of different biological mechanisms in which these entities play a role, in response to potentially harmful agents and experimental conditions. Accordingly, there is a need for improved systems and methods for analyzing system-wide biological data in view of biological mechanisms, and quantifying changes in the biological system as the system responds to an agent or a change in the environment.

SUMMARY

In one aspect, the systems and methods described herein are directed to computerized methods and one or more computer processors for quantifying the perturbation of a biological system in response to an agent.

The computerized method comprises, in one aspect, receiving, at a first processor, a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes or comprises a plurality of biological entities, each biological entity interacting with at least one other of the biological entities; receiving, at a second processor, a set of control data corresponding to the biological system not exposed to the agent; providing, at a third processor, a computational causal network model that represents the biological system and include or comprise: nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data; calculating, with a fourth processor, activity measures, for the nodes, representing a difference between the treatment data and the control data; calculating, with a fifth processor, weight values for the nodes, wherein at least one weight value is different from at least one other weight value; and generating, with a sixth processor, a score for the computational model representative of the perturbation of the biological system to the agent, wherein the score is based on the direction values, the weight values and the activity measures. The biological system may be represented by at least one mechanism hypothesis. The biological system may be represented by a plurality of computational causal network models or at least one computational causal network model comprising a plurality of mechanism hypotheses. The method may further comprise normalizing the score based on the number of measurable nodes in the respective computational model. The weight values may represent a confidence in at least one of the set of treatment data and control data. The weight values may include or comprise local false non-discovery rates. The method may further comprise calculating, with a seventh processor, an approximate distribution of the activity measures of nodes over a model or a mechanism hypotheses in a model; calculating, with an eighth processor, an expected value of activity measures with respect to the approximate distribution; and generating, with a ninth processor, a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on expected value. The approximate distribution may be based on the activity measures. In certain implementations, calculating an expected value may comprise performing a rectangular approximation. The method may further comprise calculating, with a tenth processor, a positive activation metric and a negative activation metric based on the activity measures, the positive and negative activation metrics representative of consistency and inconsistency, respectively, between the activity measures and the direction values with respect to the model; and generating, with an eleventh processor, a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on the positive and negative activation scores. The positive activation metric, negative activation metric or both may be based on local false non-discovery rates. The activity measure may be a fold-change value, and the fold-change value for each node includes or comprises a logarithm of the difference between the treatment data and the control data for the biological entity represented by the respective node. The subset of the biological system may include or comprise at least one of cell proliferation mechanism, cellular stress mechanism, cell inflammation mechanism, and DNA repair mechanism. The agent may include or comprise at least one of aerosol generated by heating tobacco, aerosol generated by combusting tobacco, tobacco smoke or cigarette smoke. The agent may include or comprise a heterogeneous substance, including a molecule or an entity that is not present in or derived from the biological system. The agent may include or comprise toxins, therapeutic compounds, stimulants, relaxants, natural products, manufactured products, and food substances. The set of treatment data may include or comprise a plurality of sets of treatment data such that each measurable node includes or comprises a plurality of fold-change values defined by a first probability distribution and a plurality of weight values defined by a second probability distribution. The set of treatment data may include or comprise a plurality of sets of treatment data such that each measurable node include or comprise a plurality of fold-change values and the corresponding weight values. The step of generating the score may comprise a linear or a non-linear combination of the activity measures, the weight values, and the direction values; and a normalization of the combination by a scale factor. The combination may be an arithmetic combination, and the scale factor is the square root of the number of biological entities for which measured data are received. The score may be generated by a geometric perturbation index scoring technique, a probabilistic perturbation index scoring technique, or an expected perturbation index scoring technique. The method may further comprise determining a confidence interval for the score based on a parametric or non-parametric computational bootstrapping technique. There is also described in another aspect, a computer system for quantifying the perturbation of a biological system in response to an agent is also described. The system comprises at least one processor configured or adapted to: receive a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes or comprises a plurality of biological entities, each biological entity interacting with at least one other of the biological entities; receive a set of control data corresponding to the biological system not exposed to the agent; provide a computational causal network model that represents the biological system and includes or comprises: nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data; calculate activity measures, for the nodes, representing a difference between the treatment data and the control data; calculate weight values for the nodes, wherein at least one weight value is different from at least one other weight value; and generate a score for the computational model representative of the perturbation of the biological system to the agent, wherein the score is based on the direction values, the weight values and the activity measures. The biological system may be represented by at least one mechanism hypothesis. The biological system may be represented by a plurality of computational causal network models or at least one computational causal network model comprising a plurality of mechanism hypotheses. The computer system may further comprises normalizing the score based on the number of scorable nodes in the respective computational model. The weight values may represent a confidence in at least one of the set of treatment data and control data. The weight values may include or comprise local false non-discovery rates. In certain implementations, the computer system further comprises calculating an approximate distribution of the activity measures of nodes over a model or a mechanism hypotheses in a model; calculating, with an eighth processor, an expected value of activity measures with respect to the approximate distribution; and generating a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on expected value. The approximate distribution may be based on the activity measures. In certain implementations of the computer system, it may further comprise calculating an expected value comprises performing a rectangular approximation. The system may further comprise calculating a positive activation metric and a negative activation metric based on the activity measures, the positive and negative activation metrics representative of consistency and inconsistency, respectively, between the activity measures and the direction values with respect to the model; and generating a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on the positive and negative activation scores. The positive activation metric, negative activation metric or both may be based on local false non-discovery rates. The activity measure may be a fold-change value, and the fold-change value for each node may include or comprise a logarithm of the difference between the treatment data and the control data for the biological entity represented by the respective node. The subset of the biological system may include or comprise at least one of cell proliferation mechanism, cellular stress mechanism, cell inflammation mechanism, and DNA repair mechanism. The agent may include or comprise at least one of aerosol generated by heating tobacco, aerosol generated by combusting tobacco, tobacco smoke or cigarette smoke. The agent may include or comprise a heterogeneous substance, including a molecule or an entity that is not present in or derived from the biological system. The agent may include or comprise toxins, therapeutic compounds, stimulants, relaxants, natural products, manufactured products, and food substances. The set of treatment data may include or comprise a plurality of sets of treatment data such that each measurable node includes or comprises a plurality of fold-change values defined by a first probability distribution and a plurality of weight values defined by a second probability distribution. The set of treatment data may include or comprise a plurality of sets of treatment data such that each measurable node includes or comprises a plurality of fold-change values and the corresponding weight values. The step of generating the score may comprise a linear or a non-linear combination of the activity measures, the weight values, and the direction values; and a normalization of the combination by a scale factor. The combination may be an arithmetic combination, and the scale factor is the square root of the number of biological entities for which measured data are received. The score may be generated by a geometric perturbation index scoring technique, a probabilistic perturbation index scoring technique, or an expected perturbation index scoring technique. The system may further comprise determining a confidence interval for the score based on a parametric or non-parametric computational bootstrapping technique. In certain aspects, the computerized method may comprise receiving, at a first processor, a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes a plurality of biological entities, each biological entity interacting with at least one other of the biological entities, and receiving, at a second processor, a set of control data corresponding to the biological system not exposed to the agent. The computerized method may comprise providing, at a third processor, a computational causal network model that represents the biological system. The computational model may include or comprise nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data. The computerized method may further comprise calculating, with a fourth processor, activity measures, for the nodes, representing a difference between the treatment data and the control data, and calculating, with a fifth processor, weight values for the nodes, wherein at least one weight value is different from at least one other weight value. The computerized method may also comprise generating, with a sixth processor, a score for the computational model representative of the perturbation of the biological system to the agent, wherein the score is based on the direction values, the weight values and the activity measures. In certain implementations, the computerized method further comprises normalizing the score based on the number of nodes in the respective computational model. In certain implementations, each of the first through sixth processors is included or comprised within a single processor or single computing device. In other implementations, one or more of the first through sixth processors are distributed across a plurality of processors or computing devices.

In certain implementations, the computational causal network model includes or comprises a set of causal relationships that exist between a node representing a potential cause and nodes representing the measured quantities. In such implementations, the activity measures may include a fold-change. The fold-change may be a number describing how much a node measurement changes going from an initial value to a final value between control data and treatment data. The fold-change number may represent the logarithm of the fold-change of the activity of the biological entity between control condition and treatment condition. The activity measure for each node may include or comprise a logarithm of the difference between the treatment data and the control data for the biological entity represented by the respective node. In such implementations, the weight value may represent a weight to be given to the fold-change value of the nodes. The weight value may represent the known biological significance of the measured node with regard to a feature or outcome of interest (e.g., a known carcinogen in cancer studies). The weight value may represent a confidence in at least one of the set of perturbation data and control data. More particularly, the weight values may include or comprise local false non-discovery rates. In such an implementation, the computerized method may generate the score for the computational model by multiplying the activity measure with the weight value and the direction value and summing over the nodes. In certain implementations, the computerized method includes or comprises generating, with a processor, a confidence interval for each of the generated scores. The confidence interval may comprise approximating a distribution of a generated score.

In another aspect, the systems and methods described herein are directed to computerized methods for quantifying the perturbation of a biological system in response to an agent. The computerized method may comprise receiving, at a first processor, a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes or comprises a plurality of biological entities, each biological entity interacting with at least one other of the biological entities, and receiving, at a second processor, a set of control data corresponding to the biological system not exposed to the agent. The computerized method may comprise providing, at a third processor, a computational causal network model that represents the biological system. The computational model may include or comprise nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data. The computerized method may further comprise calculating, with a fourth processor, activity measures, for the nodes, representing a difference between the treatment data and the control data, and calculating, with a fifth processor, an approximate distribution of the activity measures over the node. The computerized method may also include or comprise calculating, with a sixth processor, an expected value of the approximate distribution. The computerized method may also comprise generating, with a seventh processor, a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on the expected value. In certain implementations, each of the first through seventh processors is included or comprised within a single processor or single computing device. In other implementations, one or more of the first through seventh processors are distributed across a plurality of processors or computing devices.

In certain implementations, the computational causal network model includes or comprises a set of causal relationships that exist between a node representing a potential cause and nodes representing the measured quantities. In such implementations, the activity measures may include or comprise a fold-change. The fold-change may be a number describing how much a node measurement changes going from an initial value to a final value between control data and treatment data. The fold-change number may represent the logarithm of the fold-change of the activity of the biological entity between control condition and treatment condition. The computerized method may include or comprise generating, with a processor, a range for the fold-change density, which may represent an approximation of the set of values that the fold-change values can take in the biological system under the treatment conditions. The processor may generate an approximate fold-change density, which may include or comprise an approximate probability distribution of fold-change values. In such implementations, the computerized method further includes or comprises calculating the approximate expected value of the approximate fold-change density. The computerized method may generate the score for the computational model based on the calculated expected value.

In certain implementations, the approximate distributions may be based, generally, on the activity measures. Additionally and optionally, the expected value may comprise a rectangular approximation. In certain implementations, the computerized method includes or comprises generating, with a processor, a confidence interval for each of the generated scores. Generating the confidence interval may comprise performing a parametric bootstrapping technique.

In yet another aspect, the systems and methods described herein are directed to computerized methods for quantifying the perturbation of a biological system in response to an agent. The computerized method may comprise receiving, at a first processor, a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes or comprises a plurality of biological entities, each biological entity interacting with at least one other of the biological entities, and receiving, at a second processor, a set of control data corresponding to the biological system not exposed to the agent. The computerized method may comprise providing, at a third processor, a computational causal network model that represents the biological system. The computational model may include or comprise nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data. The computerized method may further comprise calculating, with a fourth processor, activity measures, for the nodes, representing a difference between the treatment data and the control data, and calculating, with a fifth processor, a positive activation score and a negative activation score based on the activity measures, the positive and negative activation scores representative of consistency and inconsistency, respectively, between the activity measures and the direction values. The computerized method may also comprise generating, with a sixth processor, a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on the positive and negative activation scores. In certain implementations, each of the first through sixth processors is included or comprised within a single processor or single computing device. In other implementations, one or more of the first through sixth processors are distributed across a plurality of processors or computing devices.

In certain implementations, the computational causal network model includes or comprises a set of causal relationships that exist between a node representing a potential cause and nodes representing the measured quantities. In such implementations, the activity measures may include or comprise a fold-change. The fold-change may be a number describing how much a node measurement changes going from an initial value to a final value between control data and treatment data. The fold-change number may represent the logarithm of the fold-change of the activity of the biological entity between control condition and treatment condition. The computerized method may include or comprise generating, with a processor, a range for the fold-change density, which may represent an approximation of the set of values that the fold-change values can take in the biological system under the treatment conditions. The computerized method may comprise calculating, with a processor, a positive activation score based on the fold-change values and the direction values. The positive and negative activation scores may indicate whether the observed activation/inhibition of biological entities is consistent or inconsistent with the expected directions of change. In one example, the positive activation score is a probability that the direction values are consistent with the activity measures. The negative activation score may be a probability that the direction values are inconsistent with the activity measures. The computerized method may further include or comprise generating a score for the computational model by combining the positive and negative activation scores. In certain implementations, the score is based on local false non-discovery rates.

In certain implementations, the subset of the biological system includes or comprises at least one of cell proliferation mechanism, cellular stress mechanism, cell inflammation mechanism, and DNA repair mechanism. The agent may include or comprise at least one of aerosol generated by heating tobacco, aerosol generated by combusting tobacco, tobacco smoke or cigarette smoke. The agent may include cadmium, mercury, chromium, nicotine, tobacco-specific nitrosamines and their metabolites (4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK), N′-nitrosonornicotine (NNN), N-nitrosoanatabine (NAT), N-nitrosoanabasine (NAB), and 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanol (NNAL)). In certain implementations, the agent includes or comprises a product used for nicotine replacement therapy. The agent may include or comprise a heterogeneous substance, including a molecule or an entity that is not present in or derived from the biological system. The agent may also include or comprise toxins, therapeutic compounds, stimulants, relaxants, natural products, manufactured products, and food substances. In certain implementations, the set of treatment data includes or comprises a plurality of sets of treatment data corresponding to certain nodes of a biological network model, wherein each such node corresponds to a plurality of fold-change values defined by a first probability distribution and a plurality of weight values defined by a second probability distribution.

In yet another aspect, the systems and methods described herein are directed to computerized methods and one or more computer processors for quantifying the perturbation of a biological system in response to an agent. The computerized method may comprise receiving, at a first processor, a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes or comprises a plurality of biological entities, each biological entity interacting with at least one other of the biological entities, and receiving, at a second processor, a set of control data corresponding to the biological system not exposed to the agent. The computerized method may comprise providing, at a third processor, a computational causal network model that represents the biological system. The computational model may include or comprise nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data. The computerized method may further comprise calculating, with a fourth processor, activity measures, for the nodes, representing a difference between the treatment data and the control data. The computerized method may also comprise generating, with a fifth processor, a score for the computational model representative of the perturbation of the biological system to the agent, wherein the score is based on the direction values and the activity measures. In certain implementations, the computerized method further comprises normalizing the score based on the number of nodes in the respective computational model. The computerized method may also comprise generating, with a sixth processor, a confidence interval for each of the generated scores. The confidence interval may comprise approximating a distribution of the generated scores and a t-statistic may be derived from the variance of the approximated distribution of generated scores. In certain implementations, each of the first through sixth processors is included or comprised within a single processor or single computing device. In other implementations, one or more of the first through sixth processors are distributed across a plurality of processors or computing devices.

The computerized methods described herein may be implemented in a computerized system having one or more computing devices, each including one or more processors. Generally, the computerized systems described herein may comprise one or more engines, which include or comprise a processing device or devices, such as a computer, microprocessor, logic device or other device or processor that is configured with hardware, firmware, and software to carry out one or more of the computerized methods described herein. In certain implementations, the computerized system includes or comprises a systems response profile engine, a network modeling engine, and a network scoring engine. The engines may be interconnected from time to time, and further connected from time to time to one or more databases, including a perturbations database, a measurables database, an experimental data database and a literature database. The computerized system described herein may include or comprise a distributed computerized system having one or more processors and engines that communicate through a network interface. Such an implementation maybe appropriate for distributed computing over multiple communication systems. In a further aspect, there is described a computer program product comprising a program code adapted to performed the method described herein. In a further aspect, there is described a computer or computer recordable medium or device comprising the computer program product.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features of the disclosure, its nature and various advantages, will be apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout, and in which:

FIG. 1 is a block diagram of an exemplary computerized system for quantifying the response of a biological network to a perturbation.

FIG. 2 is a flow diagram of an exemplary process for quantifying the response of a biological network to a perturbation by calculating a network perturbation amplitude (NPA) score.

FIG. 3 is a graphical representation of data underlying a systems response profile comprising data for two agents, two parameters, N biological entities.

FIG. 4 is an illustration of a computational model of a biological network having several biological entities and their relationships.

FIG. 5 is a flow diagram of an exemplary process for generating a geometric perturbation index (GPI) score.

FIG. 6 is a flow diagram of an exemplary process for generating a probabilistic perturbation index (PPI) score.

FIG. 7 is a flow diagram of an exemplary process for generating an expected perturbation index (EPI) score.

FIG. 8 is a flow diagram of an exemplary process for generating a confidence interval for a geometric perturbation index (GPI) score.

FIG. 9 illustrates a biological network model analyzed with the systems and methods disclosed herein.

FIGS. 10-14 illustrate network perturbation amplitude (NPA) scoring results for the network-based biological mechanisms.

FIG. 15 is a block diagram of an exemplary distributed computerized system for quantifying the impact of biological perturbations; and

FIG. 16 is a block diagram of an exemplary computing device which may be used to implement any of the components in any of the computerized systems described herein.

DETAILED DESCRIPTION

The words “including” or “comprising” do not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. Described herein are computational systems and methods that assess quantitatively the magnitude of changes within a biological system when it is perturbed by an agent. Certain implementations include or comprise methods for computing a numerical value that expresses the magnitude of changes within a portion of a biological system. The computation uses as input, a set of data obtained from a set of controlled experiments in which the biological system is perturbed by an agent. The data is then applied to a network model of a feature of the biological system. The network model is used as a substrate for simulation and analysis, and is representative of the biological mechanisms and pathways that enable a feature of interest in the biological system. The feature or some of its mechanisms and pathways may contribute to the pathology of diseases and adverse health effects of the biological system. Prior knowledge of the biological system represented in a database is used to construct the network model which is populated by data on the status of numerous biological entities under various conditions including under normal conditions and under perturbation by an agent. The network model used is dynamic in that it represents changes in status of various biological entities in response to a perturbation and can yield quantitative and objective assessments of the impact of an agent on the biological system. Computer systems for operating these computational methods are also provided.

The numerical values generated by computerized methods of the invention can be used to determine the magnitude of desirable or adverse biological effects caused by manufactured products (for safety assessment or comparisons), therapeutic compounds including nutrition supplements (for determination of efficacy or health benefits), and environmentally active substances (for prediction of risks of long term exposure and the relationship to adverse effect and onset of disease), among others.

In one aspect, the systems and methods described herein provide a computed numerical value representative of the magnitude of change in a perturbed biological system based on a network model of a perturbed biological mechanism. The numerical value referred to herein as a network perturbation amplitude (NPA) score can be used to summarily represent the status changes of various entities in a defined biological mechanism. The numerical values obtained for different agents or different types of perturbations can be used to compare relatively the impact of the different agents or perturbations on a biological mechanism which enables or manifests itself as a feature of a biological system. Thus, NPA scores may be used to measure the responses of a biological mechanism to different perturbations. The term “score” is used herein generally to refer to a value or set of values which provide a quantitative measure of the magnitude of changes in a biological system. Such a score is computed by using any of various mathematical and computational algorithms known in the art and according to the methods disclosed herein, employing one or more datasets obtained from a sample or a subject.

The NPA scores may assist researchers and clinicians in improving diagnosis, experimental design, therapeutic decision, and risk assessment. For example, the NPA scores may be used to screen a set of candidate biological mechanisms in a toxicology analysis to identify those most likely to be affected by exposure to a potentially harmful agent. By providing a measure of network response to a perturbation, these NPA scores may allow correlation of molecular events (as measured by experimental data) with phenotypes or biological outcomes that occur at the cell, tissue, organ or organism level. A clinician may use NPA values to compare the biological mechanisms affected by an agent to a patient's physiological condition to determine what health risks or benefits the patient is most likely to experience when exposed to the agent (e.g., a patient who is immuno-compromised may be especially vulnerable to agents that cause a strong immuno-suppressive response).

FIG. 1 is a block diagram of a computerized system 100 for quantifying the response of a network model to a perturbation. In particular, system 100 includes or comprises a systems response profile engine 110, a network modeling engine 112, and a network scoring engine 114. The engines 110, 112, and 114 are interconnected from time to time, and further connected from time to time to one or more databases, including a perturbations database 102, a measurables database 104, an experimental data database 106 and a literature database 108. As used herein, an engine includes or comprises a processing device or devices, such as a computer, microprocessor, logic device or other device or devices as described with reference to FIG. 14, that is configured with hardware, firmware, and software to carry out one or more computational operations.

FIG. 2 is a flow diagram of a process 200 for quantifying the response of a biological network to a perturbation by calculating a network perturbation amplitude (NPA) score, according to one implementation. The steps of the process 200 will be described as being carried out by various components of the system 100 of FIG. 1, but any of these steps may be performed by any suitable hardware or software components, local or remote, and may be arranged in any appropriate order or performed in parallel. At step 210, the systems response profile (SRP) engine 110 receives biological data from a variety of different sources, and the data itself may be of a variety of different types. The data comprises data from experiments in which a biological system is perturbed, as well as control data. At step 212, the SRP engine 110 generates systems response profiles (SRPs) which are representations of the degree to which one or more entities within a biological system change in response to the presentation of an agent to the biological system. At step 214, the network modeling engine 112 provides one or more databases that contain(s) a plurality of network models, one of which is selected as being relevant to the agent or a feature of interest. The selection can be made on the basis of prior knowledge of the mechanisms underlying the biological functions of the system. In certain implementations, the network modeling engine 112 may extract causal relationships between entities within the system using the systems response profiles, networks in the database, and networks previously described in the literature, thereby generating, refining or extending a network model. At step 216, the network scoring engine 114 generates NPA scores for each perturbation using the network identified at step 214 by the network modeling engine 112 and the SRPs generated at step 212 by the SRP engine 110. An NPA score quantifies a biological response to a perturbation or treatment (represented by the SRPs) in the context of the underlying relationships between the biological entities (represented by the network). The following description is divided into subsections for clarity of disclosure, and not by way of limitation.

A. Biological System

A biological system in the context of the present invention is an organism or a part of an organism, including functional parts, the organism being referred to herein as a subject. The subject is generally a mammal, including a human. The subject can be an individual human being in a human population. The term “mammal” as used herein includes or comprises but is not limited to a human, non-human primate, mouse, rat, dog, cat, cow, sheep, horse, and pig. Mammals other than humans can be advantageously used as subjects that can be used to provide a model of a human disease. The non-human subject can be unmodified, a transgenic animal, a genetically modified animal, or an animal carrying one or more genetic mutation(s), or silenced gene(s). A subject can be male or female. Depending on the objective of the operation, a subject can be one that has been exposed to an agent of interest. A subject can be one that has been exposed to an agent over an extended period of time, optionally including time prior to the study. A subject can be one that had been exposed to an agent for a period of time but is no longer in contact with the agent. A subject can be one that has been diagnosed or identified as having a disease. A subject can be one who has already undergone, or is undergoing treatment of a disease or adverse health condition. A subject can also be one who exhibits one or more symptoms or risk factors for a specific health condition or disease. A subject can be one that is predisposed to but is asymptomatic for a disease. In certain implementations, the disease or health condition in question is associated with exposure to an agent or use of an agent over an extended period of time. According to some implementations, the system 100 (FIG. 1) contains or generates computerized models of one or more biological systems and mechanisms of its functions (collectively, “biological networks” or “network models”) that are relevant to a type of perturbation or an outcome of interest.

Depending on the context of the operation, the biological system can be defined at different levels as it relates to the function of an individual organism in a population, an organism generally, an organ, a tissue, a cell type, an organelle, a cellular component, or a specific individual's cell(s). Each biological system comprises one or more biological mechanisms or pathways, the operation of which manifest as functional features of the system. Animal systems that reproduce defined features of a human health condition and that are suitable for exposure to an agent of interest are preferred biological systems. Cellular and organotypical systems that reflect the cell types and tissue involved in a disease etiology or pathology are also preferred biological systems. Priority could be given to primary cells or organ cultures that recapitulate as much as possible the human biology in vivo. It is also important to match the human cell culture in vitro with the most equivalent culture derived from the animal models in vivo. This enables creation of a translational continuum from animal model to human biology in vivo using the matched systems in vitro as reference systems. Accordingly, the biological system contemplated for use with the systems and methods described herein can be defined by, without limitation, functional features (biological functions, physiological functions, or cellular functions), organelle, cell type, tissue type, organ, development stage, or a combination of the foregoing. Examples of biological systems include or comprise, but are not limited to, the pulmonary, integument, skeletal, muscular, nervous (central and peripheral), endocrine, cardiovascular, immune, circulatory, respiratory, urinary, renal, gastrointestinal, colorectal, hepatic and reproductive systems. Other examples of biological systems include or comprise, but are not limited to, the various cellular functions in epithelial cells, nerve cells, blood cells, connective tissue cells, smooth muscle cells, skeletal muscle cells, fat cells, ovum cells, sperm cells, stem cells, lung cells, brain cells, cardiac cells, laryngeal cells, pharyngeal cells, esophageal cells, stomach cells, kidney cells, liver cells, breast cells, prostate cells, pancreatic cells, islet cells, testes cells, bladder cells, cervical cells, uterus cells, colon cells, and rectum cells. Some of the cells may be cells of cell lines, cultured in vitro or maintained in vitro indefinitely under appropriate culture conditions. Examples of cellular functions include or comprise, but are not limited to, cell proliferation (e.g., cell division), degeneration, regeneration, senescence, control of cellular activity by the nucleus, cell-to-cell signaling, cell differentiation, cell de-differentiation, secretion, migration, phagocytosis, repair, apoptosis, and developmental programming. Examples of cellular components that can be considered as biological systems include or comprise, but are not limited to, the cytoplasm, cytoskeleton, membrane, ribosomes, mitochondria, nucleus, endoplasmic reticulum (ER), Golgi apparatus, lysosomes, DNA, RNA, proteins, peptides, and antibodies.

B. Perturbation

A perturbation in a biological system can be caused by one or more agents over a period of time through exposure or contact with one or more parts of the biological system. An agent can be a single substance or a mixture of substances, including a mixture in which not all constituents are identified or characterized. The chemical and physical properties of an agent or its constituents may not be fully characterized. An agent can be defined by its structure, its constituents, or a source that under certain conditions produces the agent. An example of an agent is a heterogeneous substance, that is a molecule or an entity that is not present in or derived from the biological system, and any intermediates or metabolites produced therefrom after contacting the biological system. An agent can be a carbohydrate, protein, lipid, nucleic acid, alkaloid, vitamin, metal, heavy metal, mineral, oxygen, ion, enzyme, hormone, neurotransmitter, inorganic chemical compound, organic chemical compound, environmental agent, microorganism, particle, environmental condition, environmental force, or physical force. Non-limiting examples of agents include or comprise but are not limited to nutrients, metabolic wastes, poisons, narcotics, toxins, therapeutic compounds, stimulants, relaxants, natural products, manufactured products, food substances, pathogens (prion, virus, bacteria, fungi, protozoa), particles or entities whose dimensions are in or below the micrometer range, by-products of the foregoing and mixtures of the foregoing. Non-limiting examples of a physical agent include or comprise radiation, electromagnetic waves (including sunlight), increase or decrease in temperature, shear force, fluid pressure, electrical discharge(s) or a sequence thereof, or trauma.

Some agents may not perturb a biological system unless it is present at a threshold concentration or it is in contact with the biological system for a period of time, or a combination of both. Exposure or contact of an agent resulting in a perturbation may be quantified in terms of dosage. Thus, a perturbation can result from a long-term exposure to an agent. The period of exposure can be expressed by units of time, by frequency of exposure, or by the percentage of time within the actual or estimated life span of the subject. A perturbation can also be caused by withholding an agent (as described above) from or limiting supply of an agent to one or more parts of a biological system. For example, a perturbation can be caused by a decreased supply of or a lack of nutrients, water, carbohydrates, proteins, lipids, alkaloids, vitamins, minerals, oxygen, ions, an enzyme, a hormone, a neurotransmitter, an antibody, a cytokine, light, or by restricting movement of certain parts of an organism, or by constraining or requiring exercise.

An agent may cause different perturbations depending on which part(s) of the biological system is exposed and the exposure conditions. Non-limiting examples of an agent may include or comprise aerosol generated by heating tobacco, aerosol generated by combusting tobacco, tobacco smoke or cigarette smoke, and any of the gaseous constituents or particulate constituents thereof. Further non-limiting examples of an agent include or comprise cadmium, mercury, chromium, nicotine, tobacco-specific nitrosamines and their metabolites (4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK), N′-nitrosonornicotine (NNN), N-nitrosoanatabine (NAT), N-nitrosoanabasine (NAB), 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanol (NNAL)), and any product used for nicotine replacement therapy. An exposure regimen for an agent or complex stimulus should reflect the range and circumstances of exposure in everyday settings. A set of standard exposure regimens can be designed to be applied systematically to equally well-defined experimental systems. Each assay could be designed to collect time and dose-dependent data to capture both early and late events and ensure a representative dose range is covered. However, it will be understood by one of ordinary skill in the art that the systems and methods described herein may be adapted and modified as is appropriate for the application being addressed and that the systems and methods designed herein may be employed in other suitable applications, and that such other additions and modifications will not depart from the scope thereof.

In various implementations, high-throughput system-wide measurements for gene expression, protein expression or turnover, microRNA expression or turnover, post-translational modifications, protein modifications, translocations, antibody production metabolite profiles, or a combination of two or more of the foregoing are generated under various conditions including the respective controls. Functional outcome measurements are desirable in the methods described herein as they can generally serve as anchors for the assessment and represent clear steps in a disease etiology.

A “sample” as used herein refers to any biological sample that is isolated from a subject or an experimental system (e.g., cell, tissue, organ, or whole animal). A sample can include or comprise, without limitation, a single cell or multiple cells, cellular fraction, tissue biopsy, resected tissue, tissue extract, tissue, tissue culture extract, tissue culture medium, exhaled gases, whole blood, platelets, serum, plasma, erythrocytes, leucocytes, lymphocytes, neutrophils, macrophages, B cells or a subset thereof, T cells or a subset thereof, a subset of hematopoietic cells, endothelial cells, synovial fluid, lymphatic fluid, ascites fluid, interstitial fluid, bone marrow, cerebrospinal fluid, pleural effusions, tumor infiltrates, saliva, mucous, sputum, semen, sweat, urine, or any other bodily fluids. Samples can be obtained from a subject by means including but not limited to venipuncture, excretion, biopsy, needle aspirate, lavage, scraping, surgical resection, or other means known in the art.

During operation, for a given biological mechanism, an outcome, a perturbation, or a combination of the foregoing, the system 100 can generate a network amplitude (NPA) value, which is a quantitative measure of changes in the status of biological entities in a network in response to a treatment condition.

The system 100 (FIG. 1) comprises one or more computerized network model(s) that are relevant to the health condition, disease, or biological outcome, of interest. One or more of these network models are based on prior biological knowledge and can be uploaded from an external source and curated within the system 100. The models can also be generated de novo within the system 100 based on measurements. Measurable elements are causally integrated into biological network models through the use of prior knowledge. Described below are the types of data that represent changes in a biological system of interest that can be used to generate or refine a network model, or that represent a response to a perturbation.

Referring to FIG. 2, at step 210, the systems response profile (SRP) engine 110 receives biological data. The SRP engine 110 may receive this data from a variety of different sources, and the data itself may be of a variety of different types. The biological data used by the SRP engine 110 may be drawn from the literature, databases (including data from preclinical, clinical and post-clinical trials of pharmaceutical products or medical devices), genome databases (genomic sequences and expression data, e.g., Gene Expression Omnibus by National Center for Biotechnology Information or ArrayExpress by European Bioinformatics Institute (Parkinson et al. 2010, Nucl. Acids Res., doi: 10.1093/nar/gkq1040. Pubmed ID 21071405)), commercially available databases (e.g., Gene Logic, Gaithersburg, Md., USA) or experimental work. The data may include or comprise raw data from one or more different sources, such as in vitro, ex vivo or in vivo experiments using one or more species that are specifically designed for studying the effect of particular treatment conditions or exposure to particular agents. In vitro experimental systems may include or comprise tissue cultures or organotypical cultures (three-dimensional cultures) that represent key aspects of human disease. In such implementations, the agent dosage and exposure regimens for these experiments may substantially reflect the range and circumstances of exposures that may be anticipated for humans during normal use or activity conditions, or during special use or activity conditions. Experimental parameters and test conditions may be selected as desired to reflect the nature of the agent and the exposure conditions, molecules and pathways of the biological system in question, cell types and tissues involved, the outcome of interest, and aspects of disease etiology. Particular animal-model-derived molecules, cells or tissues may be matched with particular human molecule, cell or tissue cultures to improve translatability of animal-based findings.

The data received by SRP engine 110 many of which are generated by high-throughput experimental techniques, include or comprise but are not limited to that relating to nucleic acid (e.g., absolute or relative quantities of specific DNA or RNA species, changes in DNA sequence, RNA sequence, changes in tertiary structure, or methylation pattern as determined by sequencing, hybridization—particularly to nucleic acids on microarray, quantitative polymerase chain reaction, or other techniques known in the art), protein/peptide (e.g., absolute or relative quantities of protein, specific fragments of a protein, peptides, changes in secondary or tertiary structure, or posttranslational modifications as determined by methods known in the art) and functional activities (e.g., enzymatic activities, proteolytic activities, transcriptional regulatory activities, transport activities, binding affinities to certain binding partners) under certain conditions, among others. Modifications including posttranslational modifications of protein or peptide can include or comprise, but are not limited to, methylation, acetylation, farnesylation, biotinylation, stearoylation, formylation, myristoylation, palmitoylation, geranylgeranylation, pegylation, phosphorylation, sulphation, glycosylation, sugar modification, lipidation, lipid modification, ubiquitination, sumolation, disulphide bonding, cysteinylation, oxidation, glutathionylation, carboxylation, glucuronidation, and deamidation. In addition, a protein can be modified posttranslationally by a series of reactions such as Amadori reactions, Schiff base reactions, and Maillard reactions resulting in glycated protein products.

The data may also include or comprise measured functional outcomes, such as but not limited to those at a cellular level including cell proliferation, developmental fate, and cell death, at a physiological level, lung capacity, blood pressure, exercise proficiency. The data may also include or comprise a measure of disease activity or severity, such as but not limited to tumor metastasis, tumor remission, loss of a function, and life expectancy at a certain stage of disease. Disease activity can be measured by a clinical assessment the result of which is a value, or a set of values that can be obtained from evaluation of a sample (or population of samples) from a subject or subjects under defined conditions. A clinical assessment can also be based on the responses provided by a subject to an interview or a questionnaire.

This data may have been generated expressly for use in determining a systems response profile, or may have been produced in previous experiments or published in the literature. Generally, the data includes or comprises information relating to a molecule, biological structure, physiological condition, genetic trait, or phenotype. In some implementations, the data includes or comprises a description of the condition, location, amount, activity, or substructure of a molecule, biological structure, physiological condition, genetic trait, or phenotype. As will be described later, in a clinical setting, the data may include or comprise raw or processed data obtained from assays performed on samples obtained from human subjects or observations on the human subjects, exposed to an agent.

At step 212, the systems response profile (SRP) engine 110 generates systems response profiles (SRPs) based on the biological data received at step 212. This step may include or comprise one or more of background correction, normalization, fold-change calculation, significance determination and identification of a differential response (e.g., differentially expressed genes). SRPs are representations that express the degree to which one or more measured entities within a biological system (e.g., a molecule, a nucleic acid, a peptide, a protein, a cell, etc.) are individually changed in response to a perturbation applied to the biological system (e.g., an exposure to an agent). In one example, to generate an SRP, the SRP engine 110 collects a set of measurements for a given set of parameters (e.g., treatment or perturbation conditions) applied to a given experimental system (a “system-treatment” pair). FIG. 3 illustrates two SRPs: SRP 302 that includes or comprises biological activity data for N different biological entities undergoing a first treatment 306 with varying parameters (e.g., dose and time of exposure to a first treatment agent), and an analogous SRP 304 that includes or comprises biological activity data for the N different biological entities undergoing a second treatment 308. The data included or comprised in an SRP may be raw experimental data, processed experimental data (e.g., filtered to remove outliers, marked with confidence estimates, averaged over a number of trials), data generated by a computational biological model, or data taken from the scientific literature. An SRP may represent data in any number of ways, such as an absolute value, an absolute change, a fold-change, a logarithmic change, a function, and a table. The SRP engine 110 passes the SRPs to the network modeling engine 112.

While the SRPs derived in the previous step represent the experimental data from which the magnitude of network perturbation will be determined, it is the biological network models that are the substrate for computation and analysis. This analysis requires development of a detailed network model of the mechanisms and pathways relevant to a feature of the biological system. Such a framework provides a layer of mechanistic understanding beyond examination of gene lists that have been used in more classical gene expression analysis. A network model of a biological system is a mathematical construct that is representative of a dynamic biological system and that is built by assembling quantitative information about various basic properties of the biological system.

Construction of such a network is an iterative process. Delineation of boundaries of the network is guided by literature investigation of mechanisms and pathways relevant to the process of interest (e.g., cell proliferation in the lung). Causal relationships describing these pathways are extracted from prior knowledge to nucleate a network. The literature-based network can be verified using high-throughput data sets that contain the relevant phenotypic endpoints. SRP engine 110 can be used to analyze the data sets, the results of which can be used to confirm, refine, or generate network models.

C. Networks

Returning to FIG. 2, at step 214, the network modeling engine 112 uses the systems response profiles from the SRP engine 110 with a network model based on the mechanism(s) or pathway(s) underlying a feature of a biological system of interest. In certain aspects, the network modeling engine 112 is used to identify networks already generated based on SRPs. The network modeling engine 112 may include or comprise components for receiving updates and changes to models. The network modeling engine 112 may also iterate the process of network generation, incorporating new data and generating additional or refined network models. The network modeling engine 112 may also facilitate the merging of one or more datasets or the merging of one or more networks. The set of networks drawn from a database may be manually supplemented by additional nodes, edges, or entirely new networks (e.g., by mining the text of literature for description of additional genes directly regulated by a particular biological entity). These networks contain features that may enable process scoring. Network topology is maintained; networks of causal relationships can be traced from any point in the network to a measurable entity. Further, the models are dynamic and the assumptions used to build them can be modified or restated and enable adaptability to different tissue contexts and species. This allows for iterative testing and improvement as new knowledge becomes available. The network modeling engine 112 may remove nodes or edges that have low confidence or which are the subject of conflicting experimental results in the scientific literature. The network modeling engine 112 may also include or comprise additional nodes or edges that may be inferred using supervised or unsupervised learning methods (e.g., metric learning, matrix completion, pattern recognition).

In certain aspects, a biological system is modeled as a mathematical graph consisting of vertices (or nodes) and edges that connect the nodes. For example, FIG. 4 illustrates a simple network 400 with 9 nodes (including nodes 402 and 404) and edges (406 and 408). The nodes can represent biological entities or processes within a biological system, such as, but not limited to, compounds, DNA, RNA, genes, proteins, peptides, antibodies, cells, tissues, organs and cellular or molecular processes. The biological entities are not necessarily limited to those biological entities for which treatment or control data are received or available. Thus, the nodes representing the biological entities can include or comprise the plurality of biological entities and may include or comprise one or more further biological entities. At least some of the nodes are scorable and the score may represent the activity level of the node(s). Many of the nodes represent biological entities of which the activity levels can be measured. However, in some implantations, it is not necessary for the computerized method to receive data for all such measurable nodes. Thus, the nodes are scorable and/or measurable. In certain implementations, most of the nodes are measurable. A measurable node may contain or comprise measured data. The edges can represent relationships between the nodes. The edges in the graph can represent various relations between the nodes. For example, edges may represent a “binds to” relation, an “is expressed in” relation, an “are co-regulated based on expression profiling” relation, an “inhibits” relation, a “co-occur in a manuscript” relation, or “share structural element” relation. Generally, these types of relationships describe a relationship between a pair of nodes. The nodes in the graph can also represent relationships between nodes. Thus, it is possible to represent relationships between relationships, or relationships between a relationship and another type of biological entity represented in the graph. For example a relationship between two nodes that represent chemicals may represent a reaction. This reaction may be a node in a relationship between the reaction and a chemical that inhibits the reaction.

A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge. Alternatively, the edges of a graph may be directed from one vertex to another. For example, in a biological context, transcriptional regulatory networks and metabolic networks may be modeled as a directed graph. In a graph model of a transcriptional regulatory network, nodes would represent genes with edges denoting the transcriptional relationships between them. As another example, protein-protein interaction networks describe direct physical interactions between the proteins in an organism's proteome and there is often no direction associated with the interactions in such networks. Thus, these networks may be modeled as undirected graphs. Certain networks may have both directed and undirected edges. The entities and relationships (i.e., the nodes and edges) that make up a graph, may be stored as a web of interrelated nodes in a database in system 100.

The knowledge represented within the database may be of various different types, drawn from various different sources. For example, certain data may represent a genomic database, including information on genes, and relations between them. In such an example, a node may represent an oncogene, while another node connected to the oncogene node may represent a gene that inhibits the oncogene. The data may represent proteins, and relations between them, diseases and their interrelations, and various disease states. There are many different types of data that can be combined in a graphical representation. The computational models may represent a web of relations between nodes representing knowledge in, e.g., a DNA dataset, an RNA dataset, a protein dataset, an antibody dataset, a cell dataset, a tissue dataset, an organ dataset, a medical dataset, an epidemiology dataset, a chemistry dataset, a toxicology dataset, a patient dataset, and a population dataset. As used herein, a dataset is a collection of numerical values resulting from evaluation of a sample (or a group of samples) under defined conditions. Datasets can be obtained, for example, by experimentally measuring quantifiable entities of the sample; or alternatively, or from a service provider such as a laboratory, a clinical research organization, or from a public or proprietary database. Datasets may contain data and biological entities represented by nodes, and the nodes in each of the datasets may be related to other nodes in the same dataset, or in other datasets. Moreover, the network modeling engine 112 may generate computational models that represent genetic information, in, e.g., DNA, RNA, protein or antibody dataset, to medical information, in medical dataset, to information on individual patients in patient dataset, and on entire populations, in epidemiology dataset. In addition to the various datasets described above, there may be many other datasets, or types of biological information that may be included or comprised when generating a computation model. For example, a database could further include or comprise medical record data, structure/activity relationship data, information on infectious pathology, information on clinical trials, exposure pattern data, data relating to the history of use of a product, and any other type of life science-related information.

The network modeling engine 112 may generate one or more network models representing, for example, the regulatory interaction between genes, interaction between proteins or complex bio-chemical interactions within a cell or tissue. The networks generated by the network modeling engine 112 may include or comprise static and dynamic models. The network modeling engine 112 may employ any applicable mathematical schemes to represent the system, such as hyper-graphs and weighted bipartite graphs, in which two types of nodes are used to represent reactions and compounds. The network modeling engine 112 may also use other inference techniques to generate network models, such as an analysis based on over-representation of functionally-related genes within the differentially expressed genes, Bayesian network analysis, a graphical Gaussian model technique or a gene relevance network technique, to identify a relevant biological network based on a set of experimental data (e.g., gene expression, metabolite concentrations, cell response, etc.). The biological system may be represented by a plurality of network models, including computational causal network models.

As described above, the network model is based on mechanisms and pathways that underlie the functional features of a biological system. The network modeling engine 112 may generate or contain a model representative of an outcome regarding a feature of the biological system that is relevant to the study of the long-term health risks or health benefits of agents. Accordingly, the network modeling engine 112 may generate or contain a network model for various mechanisms of cellular function, particularly those that relate or contribute to a feature of interest in the biological system, including but not limited to cellular proliferation, cellular stress, cellular regeneration, apoptosis, DNA damage/repair or inflammatory response. In other embodiments, the network modeling engine 112 may contain or generate computational models that are relevant to acute systemic toxicity, carcinogenicity, dermal penetration, cardiovascular disease, pulmonary disease, ecotoxicity, eye irrigation/corrosion, genotoxicity, immunotoxicity, neurotoxicity, pharmacokinetics, drug metabolism, organ toxicity, reproductive and developmental toxicity, skin irritation/corrosion or skin sensitization. Generally, the network modeling engine 112 may contain or generate computational models for status of nucleic acids (DNA, RNA, SNP, siRNA, miRNA, RNAi), proteins, peptides, antibodies, cells, tissues, organs, and any other biological entity, and their respective interactions. In one example, computational network models can be used to represent the status of the immune system and the functioning of various types of white blood cells during an immune response or an inflammatory reaction. In other examples, computational network models could be used to represent the performance of the cardiovascular system and the functioning and metabolism of endothelial cells.

In some implementations of the present invention, the network is drawn from a database of causal biological knowledge. This database may be generated by performing experimental studies of different biological mechanisms to extract relationships between mechanisms (e.g., activation or inhibition relationships), some of which may be causal relationships, and may be combined with a commercially-available database such as the Genstruct Technology Platform or the Selventa Knowledgebase, curated by Selventa Inc. of Cambridge, Mass., USA. Using a database of causal biological knowledge, the network modeling engine 112 may identify a network that links the perturbations 102 and the measurables 104. In certain implementations, the network modeling engine 112 extracts causal relationships between biological entities using the systems response profiles from the SRP engine 110 and networks previously generated in the literature. The database may be further processed to remove logical inconsistencies and generate new biological knowledge by applying homologous reasoning between different sets of biological entities, among other processing steps.

In certain implementations, the network model extracted from the database is based on reverse causal reasoning (RCR), an automated reasoning technique that processes networks of causal relationships to formulate mechanism hypotheses, and then evaluates those mechanism hypotheses against datasets of differential measurements. Each mechanism hypothesis links a biological entity to measurable quantities that it can influence. At least one mechanism hypothesis may be formulated—such as a plurality of mechanism hypotheses. For example, measurable quantities can include or comprise an increase or decrease in concentration, number or relative abundance of a biological entity, activation or inhibition of a biological entity, or changes in the structure, function or logical of a biological entity, among others. RCR uses a directed network of experimentally-observed causal interactions between biological entities as a substrate for computation. The directed network may be expressed in Biological Expression Language™ (BEL™), a syntax for recording the inter-relationships between biological entities. The RCR computation specifies certain constraints for network model generation, such as but not limited to path length (the maximum number of edges connecting an upstream node and downstream nodes), and possible causal paths that connect the upstream node to downstream nodes. The output of RCR is a set of mechanism hypotheses that represent upstream controllers of the differences in experimental measurements, ranked by statistics that evaluate relevance and accuracy. The mechanism hypotheses output can be assembled into causal chains and larger networks to interpret the dataset at a higher level of interconnected mechanisms and pathways.

One type of mechanism hypothesis comprises a set of causal relationships that exist between a node representing a potential cause (the upstream node or controller) and nodes representing the measured quantities (the downstream nodes). The mechanism hypothesis can be used to make predictions, such as if the abundance of an entity represented by an upstream node increases, the downstream nodes linked by causal increase relationships would be inferred to be increase, and the downstream nodes linked by causal decrease relationships would be inferred to decrease.

A mechanism hypothesis represents the relationships between a set of measured data, for example, gene expression data, and a biological entity that is a known controller of those genes. Additionally, these relationships include or comprise the sign (positive or negative) of influence between the upstream entity and the differential expression of the downstream genes. The downstream genes of a hypothesis are drawn from a database of literature-curated causal biological knowledge. The causal relationships of a mechanism hypothesis that link the upstream entity to downstream genes, in the form of a computable causal network model, are the substrate for the calculation of network changes by the NPA scoring methods. The biological system may be represented by at least one mechanism hypothesis—such as a plurality of mechanism hypotheses. The at least one computational causal network model may comprise a plurality of mechanism hypotheses.

A scorable complex causal network model of biological entities can be transformed into a single causal network model by collecting the individual mechanism hypothesis representing entities in the model and regrouping the connections of all the downstream genes to a single upstream process representing the whole complex causal network model; this in essence is a flattening of the underlying graph structure. In this fashion, the activity changes of the biological entities described by the network model can be assessed via combination of its individual mechanism hypotheses, such that the underlying gene expression measurements contribute to the network as a whole.

To generate a scorable network for use in the methods of the invention, a reference node is first selected from a starting, typically complex, causal network model. The reference node can be any entity in the network whose level or activity is positively related to the activity of the network as a whole (as opposed to, for example, and inhibitor whose activity may be negatively related to the network activity). Next, the causal relationship between each node in the model and the reference node is determined. This can be done by first requiring that the model be “causally consistent”. The signs of regulation of downstream measurable entities (in this example, gene expressions) for each node in the model are adjusted based on the relationship between that model node and the reference node. For example, the signs of the downstream gene expressions for a model node that has a positive causal relationship with the reference node (i.e., that node is expected to be positively regulated when the reference node increases) are maintained. On the other hand, the signs of the downstream gene expressions for a model node with a negative causal relationship with the reference node (i.e., that node is expected to be negatively regulated when the reference node increases) are inverted. All the downstream gene expressions and their signs are then assembled into a single mechanism hypothesis, and downstream gene expressions with contradictory signs (from multiple model nodes) are omitted from the mechanism hypothesis.

For a network model to be causally consistent, for an increase in any node in the model, it should be possible to unambiguously map a sign of “positive regulation” or “negative regulation” on every other node in the model by following the causal relationships that connect the nodes. Biological interpretation can be used to resolve ambiguities to construct causally consistent models by considering what process is being scored by the mechanism hypothesis, and in what sign each node is effectively related to the reference node. For example, the node where a negative feedback connects back to the model has a particular relationship with the process being scored, and although the negative feedback may regulate this node, it should not change this relationship. Thus, the connection between the negative feedback loop and this node can be removed from the model to obtain causal consistency in a manner that is congruent with known facts. Variations on the approach described above are discussed in U.S. Patent Application Publication No. 2007/0225956 and 2009/0099784, which are incorporated by reference herein in their entirety. An exemplary causal network model is described in Westra J W, Schlage W K, Frushour B P, Gebel S, Catlett N L, Han W, Eddy S F, Hengstermann A, Matthews A L, Mathis C, et al: Construction of a Computable Cell Proliferation Network Focused on Non-Diseased Lung Cells. BMC Syst Biol 2011, 5:105, which is incorporated by reference herein in its entirety.

In certain implementations, the system 100 may contain or generate a computerized model for the mechanism of cell proliferation when the cells have been exposed to cigarette smoke. In such an example, the system 100 may also contain or generate one or more network models representative of the various health conditions relevant to cigarette smoke exposure, including but not limited to cancer, pulmonary diseases and cardiovascular diseases. In certain aspects, these network models are based on at least one of the perturbations applied (e.g., exposure to an agent), the responses under various conditions, the measurable quantities of interest, the outcome being studied (e.g., cell proliferation, cellular stress, inflammation, DNA repair), experimental data, clinical data, epidemiological data, and literature.

As an illustrative example, the network modeling engine 112 may be configured for generating a network model of cellular stress. The network modeling engine 112 may receive networks describing relevant mechanisms involved in the stress response known from literature databases. The network modeling engine 112 may select one or more networks based on the biological mechanisms known to operate in response to stresses in pulmonary and cardiovascular contexts. In certain implementations, the network modeling engine 112 identifies one or more functional units within a biological system and builds a larger network model by combining smaller networks based on their functionality. In particular, for a cellular stress model, the network modeling engine 112 may consider functional units relating to responses to oxidative, genotoxic, hypoxic, osmotic, xenobiotic, and shear stresses. Therefore, the network components for a cellular stress model may include or comprise xenobiotic metabolism response, genotoxic stress, endothelial shear stress, hypoxic response, osmotic stress and oxidative stress. The network modeling engine 112 may also receive content from computational analysis of publicly available transcriptomic data from stress relevant experiments performed in a particular group of cells.

When generating a network model of a biological mechanism, the network modeling engine 112 may include or comprise one or more rules. Such rules may include or comprise rules for selecting network content, types of nodes, and the like. The network modeling engine 112 may select one or more data sets from experimental data database 106, including a combination of in vitro and in vivo experimental results. The network modeling engine 112 may utilize the experimental data to verify nodes and edges identified in the literature. In the example of modeling cellular stress, the network modeling engine 112 may select data sets for experiments based on how well the experiment represented physiologically-relevant stress in non-diseased lung or cardiovascular tissue. The selection of data sets may be based on the availability of phenotypic stress endpoint data, the statistical rigor of the gene expression profiling experiments, and the relevance of the experimental context to normal non-diseased lung or cardiovascular biology, for example.

After identifying a collection of relevant networks, the network modeling engine 112 may further process and refine those networks. For example, in some implementations, multiple biological entities and their connections may be grouped and represented by a new node or nodes (e.g., using clustering or other techniques).

The network modeling engine 112 may further include or comprise descriptive information regarding the nodes and edges in the identified networks. A node may be described by its associated biological entity, an indication of whether or not the associated biological entity is a measurable quantity, or any other descriptor of the biological entity. Some of the nodes are scorable and the score may represent the activity level of the node(s). Many of the nodes represent biological entities of which the activity levels can be measured. However, in some implantations, it is not necessary for the computerized method to receive data for all such measurable nodes. Thus, the nodes are scorable and/or measurable. In certain implementations, most of the nodes are measurable. A measurable node may contain or comprise measured data. An edge may be described by the type of relationship it represents (e.g., a causal relationship such as an up-regulation or a down-regulation, a correlation, a conditional dependence or independence), the strength of that relationship, or a statistical confidence in that relationship, for example. In some implementations, for each treatment, each node that represents a measurable entity is associated with an expected direction of activity change (i.e., an increase or decrease) in response to the treatment. For example, when a bronchial epithelial cell is exposed to an agent such as tumor necrosis factor (TNF), the activity of a particular gene may increase. This increase may arise because of a direct regulatory relationship known from the literature (and represented in one of the networks identified by network modeling engine 112) or by tracing a number of regulation relationships (e.g., autocrine signaling) through edges of one or more of the networks identified by network modeling engine 112. In some cases, the network modeling engine 112 may identify an expected direction of change, in response to a particular perturbation, for each of the measurable entities. When different pathways in the network indicate contradictory expected directions of change for a particular entity, the two pathways may be examined in more detail to determine the net direction of change, or measurements of that particular entity may be discarded. In certain embodiments, direction values, for the nodes, may represent the expected direction of change between the control data and the treatment data. In certain embodiments, direction values, for the nodes, may represent the expected change in value between the control data and the treatment data. In certain embodiments, direction values, for the nodes, may represent the expected increase or decrease in value of the control data and the treatment data. Suitably, the change is representative of the change after treatment.

D. Network Perturbation Amplitude

The computational methods and systems provided herein translate SRPs into NPA scores. Experimental measurements that are identified as downstream effects of a perturbation within a network model are aggregated into a network-specific response score. Accordingly, at step 216, the network scoring engine 114 generates NPA scores for each perturbation using the networks identified at step 214 by the network modeling engine 112 and the SRPs generated at step 212 by the SRP engine 110. NPA scoring applies one or more defined algorithm(s) to an experimental dataset consisting of a series of treatment versus control comparisons, where the experimental data is filtered to represent a particular scope of biology (for example, a particular set of gene expression relationships) in the context of a defined biological network model. A NPA score quantifies a biological response to a treatment (represented by the SRPs) in the context of the underlying relationships between the biological entities (represented by the identified networks). The network scoring engine 114 includes or comprises hardware and software components for generating NPA scores for each of the networks contained in or identified by the network modeling engine 112.

The network scoring engine 114 may be configured to implement any of a number of scoring techniques. Such techniques include those that generate scalar-valued scores. Such techniques also include those that generate vector-valued scores. Vector-valued scores are indicative of the magnitude and topological distribution of the response of the network to the perturbation.

One described scoring technique is a strength scoring technique. A strength score is a scalar valued score that is a mean of the activity. A strength score is a mean of the activity observations for different entities represented in the SRP. The strength of a network response is calculated in accordance with:

$\begin{matrix} {{strength} = \frac{\sum\limits_{i}{d_{i}\beta_{i}}}{N}} & (1) \end{matrix}$

where d_(i) represents the expected direction of activity change for the entity associated with node i, β_(i) represents the log of the fold-change (i.e. the number describing how much a quantity changes going from initial to final value) of activity between the treatment and control conditions, and N is the number of nodes with associated measured biological entities. A positive strength score indicates that the SRP is matched to the expected activity change derived from the identified networks, while a negative strength score indicates that the SRP is unmatched to the expected activity change.

The score may be generated by a geometric perturbation index scoring technique, a probabilistic perturbation index scoring technique, or an expected perturbation index scoring technique. One scoring technique is the Geometric Perturbation Index (GPI) scoring technique. FIG. 5 is a flow diagram 500 of a GPI scoring technique that may be implemented by the network scoring engine 114. At step 502, the network scoring engine assembles a fold-change vector β. A fold-change is a number describing how much a measurable changes going from an initial value to a final value under different conditions, such as between the perturbation and control conditions. This fold-change vector has N components, corresponding to the number of nodes in the network with associated measured biological entities. In some implementations, the ith component of the fold-change vector, β_(i), represents the logarithm (e.g., base 2) of the fold-change of the activity of the ith measured biological entity between the perturbation and control conditions (i.e. the log of the factor by which the activity of the entity changes between the two conditions). As a result, a value of zero for β_(i) indicates that no change in activity was observed between the perturbation and control conditions. The logarithm operation need not be included, or may be replaced by any other linear or non-linear function. For example, in some implementations, β_(i) represents the fold-change in activity between perturbation conditions without a logarithm operation; in such implementations, a value of one for β_(i) indicates that no change in activity was observed between the perturbation and control conditions. It will be understood that fold-changes are simply one possible approach of quantifying an activity for use with the network scoring techniques described herein, and any other convention for expressing changes in measurables may be used. In certain embodiments, the step of generating the score may comprise a linear or a non-linear combination of the activity measures, the weight values, and the direction values; and a normalization of the combination by a scale factor. The combination may be an arithmetic combination, and the scale factor may be the square root of the number of biological entities for which measured data are received. In certain embodiments, the scores are not scalar-value scores.

At step 504, the network scoring engine 114 generates a weight vector r. The weight vector r also has N components, one for each of the components of the fold-change vector β. Each of the components r_(i) of the weight vector r represents a weight to be given to the ith observed fold-change β_(i). In some implementations, the weight represents the known biological significance of the ith measured entity with regard to a feature or an outcome of interest (e.g., a known carcinogen in cancer studies). In some implementations, the weight represents the confidence of the activity measurement of the biological entity associated with the node. By weighting the log-fold-changes by confidence estimates, fold-changes β_(i) for which confidence is low contribute less to the GPI score. Improved laboratory conditions, increased number of biological replicates, better repeatability, smaller variance, and stronger signals may all contribute to a higher confidence in a particular β_(i).

One value that may be advantageously used for weighting is the local false non-discovery rate fndr_(i) (i.e., the probability that a fold-change value β_(i) represents a departure from the underlying null hypothesis of a zero fold-change, in some cases, conditionally on the observed p-value) as described by Strimmer et al. in “A general modular framework for gene set enrichment analysis,” BMC Bioinformatics 10:47, 2009 and by Strimmer in “A unified approach to false discovery rate estimation,” BMC Bioinformatics 9:303, 2008, each of which is incorporated by reference herein in its entirety. In some implementations, fndr_(i) is calculated in accordance with

$\begin{matrix} {{{{fndr}_{i}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)} = {1 - {2{v_{i}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)}{\int_{{\beta_{i}/{S_{i}{({\beta_{1},\mspace{11mu} \ldots \mspace{14mu},\beta_{N}})}}}}^{\infty}{{t_{df}(x)}{x}}}}}},} & (2) \end{matrix}$

where fdr_(i) is the local false discovery rate (i.e., the probability that a fold-change value β_(i) does not represent a departure from the underlying null hypothesis of a zero fold-change), v_(i) is the Benjamini-Hochberg adjustment factor described by Benjamini et al. in “Controlling the false discovery rate: a practical and powerful approach to multiple testing,” Journal of the Royal Statistical Society, Series B 57:289, 1995, which is incorporated by reference herein in its entirety, p is the probability of obtaining a fold-change at least as extreme as the fold-change β_(i), that was actually observed (assuming that the null hypothesis of a zero fold-change is true), and t_(df) is a t-distribution with df degrees of freedom. Note that p is a function of β_(i) and the standard deviation S_(i). which is in turn based on all of the β_(i). In an alternative implementation, no adjustment for multiple testing is made; accordingly, v_(i)(β₁, . . . , β_(N)) is equal to 1 and the weight vector r_(i)=1−p(β_(i), S_(i)(β₁, . . . , β_(N))).

At step 506, the network scoring engine 114 uses the weight vector r to scale the fold-change vector β. The result is a scaled fold-change vector in which each component β_(i) is multiplied by its associated weight component r_(i). One way to achieve such a scaling computationally is to create an N×N diagonal matrix with the weight components r_(i) on the diagonal, and multiply that matrix by the N×1 vector β, as shown in Eq. 3:

$\begin{matrix} {\begin{bmatrix} {r_{1}\beta_{1}} \\ {r_{2}\beta_{2}} \\ \vdots \\ {r_{N}\beta_{N}} \end{bmatrix} = {\underset{\underset{{diag}{(r)}}{}}{\begin{bmatrix} r_{1} & 0 & \ldots & 0 \\ 0 & r_{2} & 0 & \vdots \\ \vdots & 0 & \ddots & 0 \\ 0 & \ldots & 0 & r_{N} \end{bmatrix}}\underset{\underset{\beta}{}}{\begin{bmatrix} \beta_{1} \\ \beta_{2} \\ \vdots \\ \beta_{N} \end{bmatrix}}}} & (3) \end{matrix}$

At step 508, the network scoring engine 114 identifies the expected directions of change for each component in the fold-change vector β. The network scoring engine 114 may do so by querying the network modeling engine 112 to retrieve the expected directions of change from the causal biological network models. The network scoring engine 114 can then assemble these expected directions of change into an N-component vector d, where the ith component of the vector d, d_(i), represents the expected direction of change (e.g., +1 for increased activity and −1 for decreased activity) for the ith measured biological entity.

At step 510, the network scoring engine 114 combines the components of the scaled fold-change vector (generated at step 506) with the expected directions of change for each component (identified at step 508). In some implementations, this combination is an arithmetic combination, wherein each of the scaled fold-changes r_(i)β_(i) are multiplied by its corresponding expected direction of change d_(i) and the result summed over all N biological entities. Mathematically, this implementation of step 510 can be represented by

$\begin{matrix} {\sum\limits_{i}{d_{i}r_{i}{\beta_{i}.}}} & (4) \end{matrix}$

In other implementations, the vectors d, r and β may be combined in any linear or non-linear manner.

At step 512, the network scoring engine 114 normalizes the combination of step 510. In some implementations, the normalization consists of multiplying by a pre-determined scale factor. One such scale factor is the square root of N, the number of biological entities. In this implementation, the GPI score can be represented by

$\begin{matrix} {{G\; P\; I} = {\frac{\sum\limits_{i}{d_{i}r_{i}\beta_{i}}}{\sqrt{N}}.}} & (5) \end{matrix}$

Other scale factors, which may or may not be pre-determined, may also be used. In certain embodiments, a causal network model (e.g., a mechanism hypothesis) can be seen as a unit sign vector s=(1, 1, −1, 1, . . . , −1)/√N in the N-dimensional downstream measurable space (where each dimension represents a downstream measurable, here gene expression, of the causal network model). The observed effect of perturbation on the downstream gene expressions is also a vector in this space. So geometrically, the amplitude of the perturbation in the causal network model can be quantified by projecting the differential log₂ expression vector onto the hypothesis unit vector. However, the downstream measurements of a causal network model come from a generic model. To deal explicitly with the specificity of data supporting an NPA score, each downstream is assigned a belief of activation, which is set to be the local false non-discovery rate (fndr_(i)=(1−fdr_(i))). It is equivalent to weight the dimensions of the downstream gene expression space according to the belief of each differential expression and therefore consider a weighted scalar product to define the geometry of the gene expression space: <s|β>_(W)=s^(T)·diag(fndr)·β. Hence, GPI=(Σs_(i)·fndr_(i)·β_(i))/√N. By weighting the differential log 2 expression with false non-discovery rate, individual differential expression values for which there is little confidence are moved closer to zero (no change), while values for which there is stronger confidence are minimally decreased. A positive GPI score indicates an upregulation of the process described by the mechanism hypotheses, a zero GPI score indicates that the process is unchanged along the direction s of the mechanism hypotheses, and a negative GPI score indicates that the process is down-regulated.

FIG. 6 is a flow diagram 600 of a Probabilistic Perturbation Index (PPI) scoring technique that may be implemented by the network scoring engine 114. As discussed above with respect to SRP engine 110 (FIG. 1) and step 212 of process 200 (FIG. 2), each SRP represents the activity (or change in activity) of a measured biological entity under a treatment condition. Each SRP, then, is associated with a number of measured activities, one for each measured biological entity. The PPI is a quantification of the probability that the biological mechanisms represented by the networks of interest are activated given the observed SRPs.

At step 602, the network scoring engine 114 assembles a fold-change vector β. This fold-change vector, representing the observed fold-changes in the activity of the N measured biological entities, may be assembled as described above with reference to step 502 of the Geometric Perturbation Index (GPI) scoring technique illustrated in FIG. 5. At step 604, the network scoring engine 114 generates a range for the fold-change density. The range for the fold-change density represents an approximation of the set of values that the fold-change values can take in the biological system under the treatment conditions, and may be approximated by the range [−W,W], where W is the theoretical expected largest absolute value of a log 2 fold-change. By choosing W this way, all observed fold-changes will fall in the range [−W,W]. For example, the maximum expected signal of a gene chip (e.g., 16 in log 2 scale) may be used as the value W.

At step 606, the network scoring engine 114 identifies the expected directions of change for each component in the fold-change vector β. This step may be performed as described above with reference to step 508 of the GPI scoring technique illustrated in FIG. 5, resulting in a set of expected directions of change d_(i) that correspond to the observed fold-changes β_(i).

At step 608, the network scoring engine 114 generates a positive activation metric. In some implementations, a positive activation metric represents the degree to which the SRPs indicate that the observed activation/inhibition of biological entities is consistent with the expected directions of change represented by the d_(i). Consistent behavior is referred to as “positive activation” herein. One positive activation metric that may be used is the probability that a network or networks is positively activated. Such a probability, referred to as PPI+, may be calculated in accordance with the following expression:

$\begin{matrix} {{{P\; P\; I^{+}} = {{\Pr ({PositivelyActivated})} = {\frac{1}{W}{\int_{0}^{W}{{\Pr \left( {{PositivelyActivated}\phi} \right)}{\phi}}}}}},} & (6) \end{matrix}$

in which

$\begin{matrix} {{\Pr \left( {{PositivelyActivated}\phi} \right)} = {\frac{1}{N}{\sum\limits_{0 < {d_{i}\beta_{i}} < \phi}{fndr}_{i}}}} & (7) \end{matrix}$

where fndr_(i) is the false non-discovery rate discussed above with reference to Eq. 1. In some implementations, the network scoring engine 114 is configured to numerically integrate the expression of Eq. 6 using a set of bins representing the values of φ between 0 and W. One set of bins that may be used are the bins [d_((i−1))β_((i−1)),d_((i)) β_((i))], where the (•) subscripts represent the values taken in order from smallest fold-change to largest fold-change and with the convention that d₍₀₎β₍₀₎=0. In such implementations, the network scoring engine 114 calculates an approximation to the positive activation metric PPI⁺ according to:

$\begin{matrix} {{P\; P\; I^{+}} \approx {\frac{1}{WN}{\sum\limits_{0 < {d_{i}\beta_{i}}}{{fndr}_{i}d_{i}{\beta_{i}.}}}}} & (8) \end{matrix}$

At step 610, the network scoring engine 114 generates a negative activation metric. In some implementations, a negative activation metric represents the degree to which the SRPs indicate that the observed activation/inhibition of biological entities is inconsistent with the expected directions of change represented by the d_(i). Inconsistent behavior is referred to as “negative activation” herein. One negative activation metric that may be used is the probability that a network or networks is negative activated. Such a probability, referred to as PPT⁻, may be calculated in accordance with the following expression:

$\begin{matrix} {{{P\; P\; I^{-}} = {{\Pr ({NegativelyActivated})} = {\frac{1}{W}{\int_{- W}^{0}{{\Pr \left( {{NegativelyActivated}\phi} \right)}{\phi}}}}}},} & (9) \end{matrix}$

in which

$\begin{matrix} {{\Pr \left( {{NegativelyActivated}\phi} \right)} = {\frac{1}{N}{\sum\limits_{\phi < {d_{i}\beta_{i}} < 0}{fndr}_{i}}}} & (10) \end{matrix}$

where fndr_(i) is the false non-discovery rate discussed above with reference to Eqs. 1 and 7. As discussed above with reference to positive activation metrics, in some implementations, the network scoring engine 114 is configured to numerically integrate the expression of Eq. 9 using a set of bins representing the values of φ between −W and 0. One set of bins that may be used are the bins [d_((i−1))β_((i−1)),d_((i)) β_((i))], where the (•) subscripts represent the values taken in order from smallest fold-change to largest fold-change and with the convention that d₍₀₎β₍₀₎=0. In such implementations, the network scoring engine 114 calculates an approximation to the negative activation metric PPI⁻ according to:

$\begin{matrix} {{PPI}^{\; -} \approx {\frac{1}{WN}{\sum\limits_{{d_{i}\beta_{i}} < 0}{f\; n\; d\; r_{i}d_{i}{\beta_{i}.}}}}} & (11) \end{matrix}$

At step 612, the network scoring engine combines the positive activation metric (generated at step 608) and the negative activation metric (generated at step 610) to generate a composite metric, referred to as the Probabilistic Perturbation Index or PPI. The combination of step 612 can be any linear or non-linear combination. In some implementations, the PPI is a weighted linear combination of the positive activation metric and the negative activation metric. For example, the network scoring engine 114 may be configured to generate a PPI in accordance with:

$\begin{matrix} {{{PPI} = {\frac{1}{2}\left( {{PPI}^{+} + {PPI}^{-}} \right)}},} & (12) \end{matrix}$

where PPI⁺ and PPI⁻ are the positive and negative activation metrics described above. The PPI generated according to Eq. 12 is related to the GPI calculated according to Eq. 5 in the following manner:

$\begin{matrix} {{GPI} = {\frac{W}{\sqrt{N}}{\left( {{PPI}^{+} - {PPI}^{-}} \right).}}} & (13) \end{matrix}$

Additionally, the network scoring engine 114 may be configured to compute the PPI of Eq. 12 by calculating the L1 norm of the vector whose ith component is defined according to:

$\begin{matrix} {\left\lbrack {\frac{1}{2{WN}}f\; n\; d\; r_{i}d_{i}\beta_{i}} \right\rbrack.} & (14) \end{matrix}$

FIG. 7 is a flow diagram 700 of an Expected Perturbation Index (EPI) scoring technique that may be implemented by the network scoring engine 114. As discussed above with respect to SRP engine 110 (FIG. 1) and step 212 of process 200 (FIG. 2), each SRP represents the activity (or change in activity) of a measured biological entity under a treatment condition. Each SRP, then, is associated with a number of measured activities, one for each measured biological entity. The EPI is a quantification of the average activity change over all biological entities represented by the SRP. Generally the measured activities represented in an SRP may be random draws from a distribution of measured activities, with the EPI representing the expected value of that distribution. If each of the fold-changes β_(i) is drawn from a distribution p(•), then the expected value of that distribution is

EPI=∫φ·p(φ)·dφ.  (15)

Since the true theoretical distribution p(•) is not readily known, the network scoring engine 114 may be configured to execute the steps described below to approximate the EPI value based on the observed activities and other information drawn from the system 100.

At step 702, the network scoring engine 114 assembles a fold-change vector β. This fold-change vector, representing the observed fold-changes in the activity of the N measured biological entities, may be assembled as described above with reference to step 502 of the Geometric Perturbation Index (GPI) scoring technique illustrated in FIG. 5 or step 602 of the Probabilistic Perturbation Index (PPI) scoring technique illustrated in FIG. 6. At step 704, the network scoring engine 114 generates a range for the fold-change density. The network scoring engine 114 may generate the range for the fold-change density as described above with reference to step 604 of the PPI scoring technique illustrated in FIG. 6.

At step 706, the network scoring engine 114 identifies the expected directions of change for each component in the fold-change vector β. This step may be performed as described above with reference to step 508 of the GPI scoring technique illustrated in FIG. 5, resulting in a set of expected directions of change d_(i) that correspond to the observed fold-changes β_(i).

At step 708, the network scoring engine 114 generates an approximate fold-change density. If each of the fold-changes β_(i) drawn from a distribution p(•), then the distribution p(•) can be approximately represented by:

$\begin{matrix} {{\hat{p}(\phi)} \propto \left\{ \begin{matrix} {{\frac{1}{N}{\sum\limits_{i|{{d_{i}\beta_{i}} > \phi}}\frac{\beta_{i}}{W}}},} & {\phi > ɛ} \\ {{\frac{1}{N}{\sum\limits_{i|{{d_{i}\beta_{i}} < \phi}}\frac{\beta_{i}}{W}}},} & {\phi < {ɛ.}} \end{matrix} \right.} & (16) \end{matrix}$

At step 710, the network scoring engine 114 generates the approximate expected value of the approximate fold-change density, resulting in an EPI score. In some implementations, the network scoring engine 114 applies a computational interpolation technique (e.g., linear or non-linear interpolation techniques) to generate an approximate continuous distribution from the distribution of Eq. 16, then calculates the expected value of that distribution using the formula of Eq. 15. In other implementations, the network scoring engine 114 is configured to use the discrete distribution of Eq. 16 as a rectangular approximation to the continuous distribution, and calculate the EPI in accordance with:

$\begin{matrix} {{EPI} \approx {\frac{1}{WN}\begin{bmatrix} {{\sum\limits_{i|{{d_{i}\beta_{i}} > 0}}{\left( {d\; \beta} \right)_{(i)}\left( {\sum\limits_{j = 1}^{n_{+}}\left( {d\; \beta} \right)_{(j)}} \right)\left( {\left( {d\; \beta} \right)_{(i)} - \left( {d\; \beta} \right)_{({i - 1})}} \right)}} -} \\ {\sum\limits_{i|{{d_{i}\beta_{i}} < 0}}{{- \left( {d\; \beta} \right)_{(i)}}\left( {\sum\limits_{j = 1}^{n_{-}}{- \left( {d\; \beta} \right)_{(j)}}} \right)\left( {{- \left( {d\; \beta} \right)_{(i)}} - \left( {- \left( {d\; \beta} \right)_{({i - 1})}} \right)} \right)}} \end{bmatrix}}} & (17) \end{matrix}$

In Eq. 17, the (•) subscripts represent the values taken in order from smallest fold-change to largest fold-change), n⁺ is the number of entities whose activity was expected to increase in response to the treatment (d_(i)β_(i)>=0) (per step 706) and n− is the number of entities whose activity was expected to decrease in response to the treatment (d_(i)β_(i)<=0) (per step 706). In the EPI score, high value fold-changes are taken into account more often than lower ones, providing a measure of activity with high specificity.

The network scoring engine 114 may also be configured to determine confidence intervals around the network scores. These confidence intervals may be used by clinicians and researchers to evaluate the experimental results reflected in the network scores and may be used by other components of the system 100 in further data processing steps (e.g., by the aggregation engine 110). One useful method for determining confidence intervals is to evaluate the null hypothesis of the network score being zero (or other appropriate null value representing no different in activity between treatment and control conditions) for a given Type-I (false positive) error risk α (e.g., α=0.05). In some implementations, the network scoring engine 114 uses a computational bootstrapping technique, such as a parametric or non-parametric bootstrapping technique, to approximate the distributions of the computed metrics. Many such bootstrapping techniques are known in the art. When few assumptions about the underlying distribution can be made, a non-parametric technique may be advantageously employed. When an underlying distribution is assumed, parametric techniques may be advantageously employed. In the examples discussed below, the β_(i) are assumed to arise from a normal distribution under the null hypothesis, with mean zero and sample variance S_(i) ² based on t_(df) degrees of freedom. The network scoring engine may generate these quantities, as well as t-statistics and moderated t-statistics representative of the β_(i), by using a statistical estimation and test procedure, such as the t-statistics and moderated t-statistics generated by the linear model approach of the “limma” R package, commonly used in the analysis of differential gene expression and described by Smyth in “Linear models and empirical Bayes methods for assessing differential expression in microarray experiments,” Statistical Applications in Genetics and Molecular Biology, 3:3, 2004, incorporated in its entirety by reference herein. For example, to determine confidence intervals for EPI scores (as discussed above with reference to FIG. 7), the network scoring engine 114 may be configured to implement a parametric bootstrapping technique to approximate the distribution of the β_(i), assuming that the β_(i) arise from an underlying normal distribution. In implementations in which the assumptions for the application of percentile bootstrapping appear to be violated, which may include or comprise EPI, the network scoring engine 114 may additionally apply the bias-corrected percentile method described by Efron in “The jackknife, the bootstrap, and other resampling plans,” SIAM, 1982 and Diciccio et al. in “A review of bootstrap confidence intervals,” Journal of the Royal Statistical Society, 50:338, 1988, each of which is incorporated by reference in its entirety herein.

In some implementations, the network scoring engine 114 may employ an analytical approach to determine the confidence intervals, instead of or in combination with a bootstrapping technique. The particular techniques implemented by the network scoring engine 114 to analytically determine confidence intervals will depend on the particular network scoring technique used and the assumptions on the underlying statistical distributions for the β_(i).

For example, when the network scoring engine 114 is configured to calculate strength scores (in accordance with Eq. 1), the network scoring engine 114 treats the strength score as a random variable consisting of a weighted sum of independent, approximately normal random variables. As a result, the distribution of the strength score is an approximately normal random variable, with zero mean and a variance that is calculated in accordance with

$\begin{matrix} {S_{strength}^{2} = {\frac{1}{N^{2}}{\sum\limits_{i}{S_{i}^{2}.}}}} & (18) \end{matrix}$

The network scoring engine 114 can use the variance S_(strength) ² to derive a t-statistic in accordance with

$\begin{matrix} {{t = \frac{strength}{S_{strength}}},} & (19) \end{matrix}$

whose degrees of freedom df is estimated with the Welch-Satterthwaite equation, described by Satterthwaite in “An approximate distribution of estimates of variance components,” Biometrics, 2:110, 1946 and by Welch in “The generalization of student's problems when several different population variances are involved,” Biometrika, 34:28, 1947, each of which is incorporated in its entirety by reference herein. Using these quantities, the network scoring engine 114 may generate a (1−α)-confidence interval for the strength score in accordance with

strength±t _(df) ^(α/2) S _(strength).  (20)

As another example, when the network scoring engine 114 is configured to calculate GPI scores (as discussed above with reference to FIG. 5), the network scoring engine 114 may also be configured to calculate a confidence interval for the GPI score in accordance with the steps of the flow diagram 800 of FIG. 8. At step 802, the network scoring engine 114 performs a first-order Taylor expansion of the GPI score as represented by Eq. 5, as a function of the β_(i), in accordance with

$\begin{matrix} {{{GPI}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)} = \left. {{{GPI}\left( {{\hat{\beta}}_{1},\ldots \mspace{14mu},{\hat{\beta}}_{N}} \right)} + {\sum\limits_{i}\frac{\partial{GPI}}{\partial\beta_{i}}}} \middle| {}_{{\hat{\beta}}_{i}}{\left( {\beta_{i} - {\hat{\beta}}_{i}} \right) + {O\left( N^{2} \right)}} \right.} & (21) \end{matrix}$

wherein β_(i) ̂hat is the measured fold-change value. The first-order Taylor approximation of the GPI score retains the first two terms and drops the O(N²) terms.

At step 804, the network scoring engine 114 assesses whether the coefficients of the β_(i) terms in the GPI calculation are functions of the β_(i). These coefficients include or comprise the expected direction terms d_(i) and the weights r_(i). When these coefficients do not depend on the values of β_(i), the first-order term in Eq. 21 becomes a constant value with respect to β_(i) and the network scoring engine 114 proceeds to step 808. However, when the coefficients do depend on the values of β_(i), the network scoring engine 114 proceeds to step 806 to approximate the first-order term in Eq. 21. In particular, when the weight vector r is a function of the β_(i) and the expected direction terms d_(i) are not a function of the β_(i), the first order term may be represented as:

$\begin{matrix} {\frac{\partial{GPI}}{\partial\beta_{i}} = {\frac{1}{\sqrt{N}}{\left( {{d_{i}r_{i}} + {d_{i}\beta_{i}\frac{\partial r_{i}}{\partial\beta_{i}}}} \right).}}} & (22) \end{matrix}$

In particular, when the weight vector r is a vector of false non-discovery rate values, fndr_(i), as discussed above with reference to Eq. 2 and step 504 of FIG. 5, the network scoring engine 114 may use the following expression for the derivative term of Eq. 22:

$\begin{matrix} {{\frac{\partial}{\partial\beta_{i}}f\; n\; d\; {r_{i}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)}} = {{{- 2}\underset{\underset{{term}\; 1}{}}{\frac{\partial{v_{i}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)}}{\partial\beta_{i}}}\underset{\underset{{term}\; 2}{}}{\int_{\frac{\beta_{i}}{S_{i}}}^{\infty}{{t_{df}(x)}\ {x}}}} - {2{v_{i}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)}\frac{\partial}{\partial\beta_{i}}{\left( {\int_{\frac{\beta_{i}}{S_{i}}}^{\infty}{{t_{df}(x)}\ {x}}} \right).}}}} & (23) \end{matrix}$

The derivative labeled “term1” in Eq. 23 represents the derivative of the Benjamini-Hochberg adjustment factor and the integral labeled “term2” represents the p-value for the fold-change of the ith biological entity. Because the Benjamini-Hochberg terms are most relevant when p-values are low, the network scoring engine 114 may be configured to approximate the product of term1 and term2 as zero at step 806. As a result, the network scoring engine 114 may apply the fundamental theorem of calculus and use the following approximation of the derivative term of Eq. 23:

$\begin{matrix} {{\frac{\partial}{\partial\beta_{i}}f\; n\; d\; {r_{i}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)}} \approx {2\mspace{11mu} {{sgn}\left( \beta_{i} \right)}\frac{v_{i}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)}{S_{i}}{{t_{df}\left( {\frac{\beta_{i}}{S_{i}}} \right)}.}}} & (24) \end{matrix}$

Including the approximation of Eq. 24 in the expression of Eq. 21 yields the following approximation of the GPI score:

$\begin{matrix} {{{GPI}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)} = {{{GPI}\left( {{\hat{\beta}}_{1},\ldots \mspace{14mu},{\hat{\beta}}_{N}} \right)} + {\left( {\beta_{i} - {\hat{\beta}}_{i}} \right) \cdot {\sum\limits_{i}{\left( {{d_{i}f\; n\; {dr}_{i}} + {d_{i}{{{\hat{\beta}}_{i}}\left\lbrack {2\frac{v_{i}\left( {{\hat{\beta}}_{1},\ldots \mspace{14mu},{\hat{\beta}}_{N}} \right)}{{\hat{S}}_{i}}{t_{df}\left( {\frac{{\hat{\beta}}_{i}}{{\hat{S}}_{i}}} \right)}} \right\rbrack}}} \right)\frac{1}{\sqrt{N}}}}}}} & (25) \end{matrix}$

At step 808, the network scoring engine 114 determines the approximate variance of the GPI score using the approximation of the GPI score generated in the preceding steps. If the GPI score has been approximated as an affine function of the random variables β_(i) (as in Eq. 21), the variance of the approximation will be the weighted sum of the variances of the β_(i) as given by:

$\begin{matrix} {{S_{GPI}^{2} = {\sum\limits_{i}{\left( \frac{\partial{GPI}}{\partial\beta_{i}} \right)^{2}S_{i}^{2}}}},} & (26) \end{matrix}$

where S_(i) ² is the variance of the ith fold-change β_(i). Thus, the variance of the approximation of Eq. 25 may be written as:

$\begin{matrix} {{S_{GPI}^{2} \approx {\sum\limits_{i}{\left( {{f\; n\; {dr}_{i}} + {{\beta_{i}}\left\lbrack {2\frac{v_{i}\left( {\beta_{1},\ldots \mspace{14mu},\beta_{N}} \right)}{{\hat{S}}_{i}}{t_{df}\left( {\frac{\beta_{i}}{{\hat{S}}_{i}}} \right)}} \right\rbrack}} \right)^{2}S_{i}^{2}\frac{1}{N}}}},} & (27) \end{matrix}$

where the d_(i) terms drop away when d_(i)=+/−1 because d_(i) ²=1.

At step 810, the network scoring engine 114 evaluates the variance of the GPI score (e.g., as represented by Eq. 27) at the observed fold-change values. At step 812, the network scoring engine 114 generates a confidence interval for the GPI score in accordance with

GPI±t _(df) ^(α/2) S _(GPI),  (28)

where S_(GPI) is calculated as described above with reference to Eqs. 26 and 27. Eq. 28 may be adapted as desired to determine variance of a PPI score at the observed fold-change values.

The network scoring engine 114 may generate vector-valued scores in addition to or instead of the scalar-valued scores described above. One vector-valued score is the vector of fold-changes or absolute changes in activity for each of the measured nodes.

In certain implementations, for each perturbation (e.g., exposure to a known or unknown agent), the network scoring engine 114 may generate multiple NPA scores. For example, the network scoring engine 114 may generate an NPA score for a particular network, a particular dose of the agent, and a particular exposure time.

E. Experimental Results

The process 200 for quantifying the response of a biological network to a perturbation by calculating a network perturbation amplitude (NPA) score has been used to analyze tumor necrosis factor (TNF)-treated normal human bronchial epithelial (NHBE) cells using several causal network models. Activation of the stress- and immune-response transcription factor NF-kB (nuclear factor kappa-light-chain enhancer of activated B cells) has been well-defined as a major mediator of tumor necrosis factor-alpha (TNFα)-induced signaling in a variety of systems. Normal human bronchial epithelial (NHBE) cells were treated with four different doses of TNFα (0.1, 1, 10 and 100 ng/mL) and total RNA was collected for microarray measurement at four different times after treatment (30 minutes, 2 hours, 4 hours and 24 hours). All treatments were compared to time-matched mock-treated controls to obtain 16 contrasts (4 doses×4 time points). Normal human bronchial epithelial cells (Lonza Walkersville, Inc.) were cultured in standard growth medium (Clonetics medium, Lonza Walkersville, Inc.). Cells were either treated with TNFα (Sigma) or a vehicle control (HBSS), and then harvested after the desired perturbation time periods. Cells were immediately put on ice and split into three technical replicates from which total RNA was extracted using RNeasy Microkit (Qiagen). The processed RNA samples are then hybridized to Affymetrix U133 Plus 2.0 microarrays. Cell viability and cell counts were controlled for all conditions after 24 hours with CellTiter-Glo® assay (Promega). NF-kB nuclear translocation was measured using Cellomics NF-kB Activation HCS Reagent Kit (Thermo Scientific). Data processing and NPA methods were implemented in the R statistical environment. Raw RNA expression data was analyzed using the affy and limma packages of the Bioconductor suite of microarray analysis tools available in the R statistical environment (Gentleman R: Bioinformatics and computational biology solutions using R and Bioconductor. New York: Springer Science+Business Media; 2005; Gentleman R C, Carey V J, Bates D M, Bolstad B, Dettling M, Dudoit S, Ellis B, Gautier L, Ge Y, Gentry J, et al: Bioconductor: open software development for computational biology and bioinformatics. Genome Biol 2004, 5:R80). Robust Microarray Analysis (RMA) background correction and quantile normalization were used to generate probe set expression values (Irizarry et al., Exploration, normalization, and summaries of high density oligonucleotide array probe level data. Biostatistics 2003, 4:249-264). An overall linear model was fit to the data for all groups of replicates, and specific contrasts of interest (comparisons of “treated” and “control” conditions) were evaluated to generate raw p-values for each probe set on the expression array. Raw p-values were subsequently corrected for multiple testing effects using Benjamini-Hochberg false discovery rate (FDR).

Probe sets were matched to RNA Abundance nodes in the Selventa Knowledgebase using the HG-U133_Plus_(—)2.na30 probe set mappings and the following criteria. First, only “at” or “s_at” probe sets were considered. Second, probe sets that mapped to multiple genes were discarded. Third, when multiple probe sets mapped to the same gene, preference was given to “at” probe sets over “s_at” probe sets. Finally, when there still remained multiple probe sets mapped to the same gene, the probe set with the lowest geometric mean FDR-corrected p-value across all contrasts of interest was selected. A linear model was then re-fit for all groups of replicates to only those probe sets that mapped to RNA Abundance nodes in the knowledgebase, and FDR-corrected p-values were recomputed. The Selventa Knowledgebase is a repository containing over 1.5 million nodes (biological concepts and entities) and over 7.5 million edges (assertions about causal and non-causal relationships between nodes). The assertions in the Selventa Knowledgebase are derived from peer-reviewed scientific literature as well as other public and proprietary databases. Specifically, each assertion describes an individual experimental observation from an experiment performed in a human, mouse, and rat species context, either in vitro or in vivo. Assertions also capture information about the referring source (e.g. the PubMed ID (PMID) for journal articles listed in MEDLINE), as well as key contextual information including the species (human, mouse, or rat) and the tissue or cell line from which the experimental observation was derived. An example causal assertion is the increased transcriptional activity of NFkB (nuclear factor kappa-light-chain-enhancer of activated B cells) causes an increase in the mRNA expression of CXCL1 (Chemokine (C-X-C motif) ligand 1) [HeLa cell line; Human; PMID 16414985]. The knowledgebase contains causal relationships derived from healthy tissues and disease areas such as inflammation, metabolic diseases, cardiovascular injury, liver injury, and cancer.

The GPI, EPI and PPI scoring methods were first investigated using a causal network model created to be a specific measure of NF-kB activation, the NF-kB-direct model. This model is composed of 155 genes (curated from 247 distinct references, some genes being supported by more than one reference) known to be directly regulated by NF-kB (genes whose expression is controlled in an NF-kB-dependent manner and whose promoter sequences are directly bound by NF-kB). Both scoring methods showed the same pattern of response to TNFα, having demonstrated a dose-dependent response at all times, and a time-dependent response that generally saturated at later times (See FIG. 10 a). The EPI method was qualitatively different from GPI in that EPI scores continued to increase from 2 hours to 4 hours to 24 hours, while the GPI score plateaued from 4 hours to 24 hours. Also, the EPI method produced near-zero scores for 0.1 ng/mL TNFα. In general, EPI scores appeared to reduce to 0 (or near to 0) scores that trended relatively lower by other methods. The lowest dose for all but the 2 hour time point for the EPI method were found to not be specific to the NF-κB-direct network model.

Next, NF-κB-direct model scores were compared to NF-κB nuclear translocation. Upon activation, NF-κB is transported into the nucleus where it acts to regulate the expression of many genes. A series of feedback loops then lead to the subsequent translocation of NF-κB back to the cytoplasm, and this oscillatory cycle continues several times. Because NF-κB oscillations occur with slightly different periods in different cells in the population, the first oscillation may be the most reliable population-measure of NF-κB activation. Although the time of the first oscillation depends on dose, 30 minutes after TNFα treatment may be a realistic time to measure NF-κB nuclear translocation for the doses used. All three scoring methods produced a monotonic, and in some cases nearly linear, relationship between score and nuclear translocation, with Pearson correlation coefficients between 0.85 and 0.98 for the GPI and EPI scoring methods (FIG. 11). FIG. 11 illustrates NF-κB-direct NPA scores at 30 minutes, plotted against NF-κB nuclear translocation at 30 minutes. Error bars in NF-κB nuclear translocation represent the standard deviation of the mean nuclear translocation for three different fields of view of the same population of cells. Interestingly, this dose-dependent relationship was preserved at different times after TNFα treatment (FIG. 13). These findings demonstrate that the causal network model-based NPA scores can quantify NF-κB transcriptional activity.

The effects of the extent and composition of a causal network model on the NPA scoring methods of the invention were also investigated. First, the effect of hand-selecting a set of measurements that are known to be modulated by NF-κB specifically in a TNFα-dependent manner was assessed. A submodel was constructed from a set of 20 genes that were previously measured via reverse transcriptase-polymerase chain reaction (RT-PCR) to assess NF-κB activity in response to TNFα treatment in 3T3 mouse fibroblast cells (omitting 2 genes that have no direct human ortholog). These genes were measured as perturbed by TNFα in 3T3 cells upon dosing with TNFα (10 different concentrations spanning 100 ng/mL to 0.005 ng/mL) over a 12 hour time course. This submodel produced a very similar pattern of activation to the NF-κB-direct model (FIG. 14), suggesting that inclusion of genes whose TNFα-dependent expression has not been directly verified does not have a detrimental effect on the quality of the score. FIG. 14 shows the results of transcriptomic data from TNFα-treated NHBE cells which was scored using GPI and EPI for (a) the NF-κB-direct model, (b) a submodel composed of 20 NF-κB-regulated genes reported to be TNFα-responsive in mouse 3T3 fibroblast cells (NFKBIA, CASP4, CCL5, TNFAIP3, CCL2, ZFP36, RIPK2, TNFSF10, NFKBIE, IL6, CCL20, ICAM1, TNFRSF1A, TNFRSF1B, SQSTM1, NRG1, SOD1, IL1RL1, HIF1A, ERBB2)(Tay et al., Single-cell NF-kappaB dynamics reveal digital activation and analogue information processing. Nature 2010, 466:267-271).

Next, the effects of using causal network models derived from upstream biological entities that are less proximal to the measurement were investigated. To do so, two additional models were constructed: the IKK/NF-κB signaling model, which is composed of 992 genes (curated from 414 different references) that are known to be modulated by perturbation of proteins in a causal network model of signaling from the IκB kinase (IKK) proteins to NF-κB activation (FIG. 9); and the TNF model, which is composed of 1741 genes (curated from 589 different references) that are known to be modulated by treatment of cells with TNFα. Whereas the NF-κB-direct model is composed entirely of genes whose expressions were directly controlled by a single transcription factor (NF-κB), each of these two models contains genes whose direct transcriptional controller is not necessarily known. The expression of these genes may be controlled by transcription factors not involved in constructing the model. For example, genes in the IKK/NF-κB signaling model are known to be modulated by perturbation of proteins in the IKK/NF-κB signaling causal network model, but some of these genes could be regulated as secondary effects caused by altered expression of a smaller subset of genes that are directly modulated by NF-κB. Also, TNFα is a ligand and therefore does not directly mediate transcription of any genes. Treatment of cells with TNFα results in activation of a myriad of transcription factors, any of which may directly or indirectly (for example, through autocrine signaling) alter the expression of each gene in the TNF model.

FIG. 9 illustrates the full causal network model (top), along with a schematic of the basic model architecture (middle). CHUK, IKBKB, and IKBKG act as inhibitors of NFKBIA, NFKBIB, and NFKBIE, which are in turn inhibitors of NFKB1, NFKB2, and RELA. The nodes used in the model are listed under each section. The nodes in bold represent nodes that have downstream gene expression measurables in the knowledgebase, and the number of measurables is given in the square brackets (because the same downstream may be found under multiple nodes, these 1227 downstream measurables correspond to 992 unique measurables). The notations used are as follows: “CHUK P@S” represents CHUK phosphorylated at serine (where the residue is given if known), “CHUK P@ST” represents CHUK phosphorylated at serine or threonine (the exact residue is unknown), “kaof(CHUK)” represents the kinase activity of CHUK, “CHUK:IKBKB” represents the complex of CHUK and IKBKB proteins, “IkappaB kinase complex Hs” represents an aggregate of the various kinases (CHUK, IKBKB, and IKBKG) in Homo sapiens (Hs), “degradationof(NFKBIA)” represents the process of NFKBIA degradation, and “taof(NFKB1)” represents the transcriptional activity of NFKB1. The IKK/NF-κB signaling model and TNF model give insight into the behaviors of mechanism hypotheses at different levels of proximity to the measurements. The IKK/NF-κB signaling model is primarily composed of genes that are regulated (either directly or indirectly) by NF-κB (FIG. 9), and it produced a pattern of response that is very similar to the NF-κB-direct model (FIG. 10( b)). This similar pattern of response suggests that there is not a large difference between the population-level behavior of genes that are known to be directly regulated by a transcription factor and the behavior of genes where knowledge of direct regulation is unknown. The time- and dose-dependent response that was seen for the NF-κB-direct model appears somewhat less robustly in the TNF model (FIG. 10( c)), for example at the 30 minute time point, but again the methods produced very similar responses. Thus, although the general pattern of response was well-preserved among the models, minor but noticeable differences in response can be observed in models that are less proximal to the entities of which measurements were made.

To assess the ability of the causal network models to respond specifically to relevant TNFα signaling perturbations, another model was constructed for a key cell-cycle component, the transcription factor E2F1, with the assumption that E2F1 is a less direct effector of TNFα signaling compared to NF-κB. The E2F1-direct model is composed of 80 genes (curated from 54 different references) known to be directly regulated by E2F1 (expression controlled by E2F1 and promoter sequence bound by E2F1). In order to provide a comparison of NPA results for biology not directly related to NF-κB signaling, the NPA response of the four models introduced above (NF-κB-direct, IKK/NF-κB signaling, TNF, and E2F1-direct) were assessed in response to inhibition of cell cycle progression via a CDK inhibitor. Specifically, a publicly available microarray data set was used for treatment of HCT116 colon cancer cells with three different concentrations of the CDK inhibitor R547 (GSE15395)(Berkofsky-Fessler, et al: Preclinical biomarkers for a cyclin-dependent kinase inhibitor translate to candidate pharmacodynamic biomarkers in phase I patients. Mol Cancer Ther 2009, 8:2517-2525)(FIG. 12). All three NPA methods demonstrated dose- and time-dependent decreases in the E2F1-direct model score at the 4 hour, 6 hour, and 24 hour time points. The TNF model showed a similar pattern of response as the E2F1-direct model. In contrast, the NF-Kκ-direct and IKK/NF-κB signaling model scores did not display this same dose- and time-dependent pattern, indicating that these focused models potentially contain few cell cycle regulated genes.

F. Hardware

FIG. 15 is a block diagram of a distributed computerized system 1500 for quantifying the impact of biological perturbations. The components of the system 1500 are the same as those in the system 100 of FIG. 1, but the arrangement of the system 100 is such that each component communicates through a network interface 1510. Such an implementation maybe appropriate for distributed computing over multiple communication systems including wireless communication system that may share access to a common network resource, such as “cloud computing” paradigms.

FIG. 16 is a block diagram of a computing device, such as any of the components of system 100 of FIG. 1 or system 1300 of FIG. 13 for performing processes described with reference to FIGS. 1-10. Each of the components of system 100, including the SRP engine 110, the network modeling engine 112, the network scoring engine 114, the aggregation engine 116 and one or more of the databases including the outcomes database, the perturbations database, and the literature database may be implemented on one or more computing devices 1600. In certain aspects, a plurality of the above-components and databases may be included or comprised within one computing device 1600. In certain implementations, a component and a database may be implemented across several computing devices 1600.

The computing device 1600 comprises at least one communications interface unit, an input/output controller 1610, system memory, and one or more data storage devices. The system memory includes or comprises at least one random access memory (RAM 1602) and at least one read-only memory (ROM 1604). All of these elements are in communication with a central processing unit (CPU 1606) to facilitate the operation of the computing device 1600. The computing device 1600 may be configured in many different ways. For example, the computing device 1600 may be a conventional standalone computer or alternatively, the functions of computing device 1600 may be distributed across multiple computer systems and architectures. The computing device 1600 may be configured to perform some or all of modeling, scoring and aggregating operations. In FIG. 10, the computing device 1600 is linked, via network or local network, to other servers or systems.

The computing device 1600 may be configured in a distributed architecture, wherein databases and processors are housed in separate units or locations. Some such units perform primary processing functions and contain at a minimum a general controller or a processor and a system memory. In such an aspect, each of these units is attached via the communications interface unit 1608 to a communications hub or port (not shown) that serves as a primary communication link with other servers, client or user computers and other related devices. The communications hub or port may have minimal processing capability itself, serving primarily as a communications router. A variety of communications protocols may be part of the system, including, but not limited to: Ethernet, SAP, SAS™, ATP, BLUETOOTH™, GSM and TCP/IP.

The CPU 1606 comprises a processor, such as one or more conventional microprocessors and one or more supplementary co-processors such as math co-processors for offloading workload from the CPU 1606. The CPU 1606 is in communication with the communications interface unit 1608 and the input/output controller 1610, through which the CPU 1606 communicates with other devices such as other servers, user terminals, or devices. The communications interface unit 1608 and the input/output controller 1610 may include or comprise multiple communication channels for simultaneous communication with, for example, other processors, servers or client terminals. Devices in communication with each other need not be continually transmitting to each other. On the contrary, such devices need only transmit to each other as necessary, may actually refrain from exchanging data most of the time, and may require several steps to be performed to establish a communication link between the devices.

The CPU 1606 is also in communication with the data storage device. The data storage device may comprise an appropriate combination of magnetic, optical or semiconductor memory, and may include or comprise, for example, RAM 1602, ROM 1604, flash drive, an optical disc such as a compact disc or a hard disk or drive. The CPU 1606 and the data storage device each may be, for example, located entirely within a single computer or other computing device; or connected to each other by a communication medium, such as a USB port, serial port cable, a coaxial cable, an Ethernet type cable, a telephone line, a radio frequency transceiver or other similar wireless or wired medium or combination of the foregoing. For example, the CPU 1606 may be connected to the data storage device via the communications interface unit 1608. The CPU 1606 may be configured to perform one or more particular processing functions.

The data storage device may store, for example, (i) an operating system 1612 for the computing device 1600; (ii) one or more applications 1614 (e.g., computer program code or a computer program product) adapted to direct the CPU 1606 in accordance with the systems and methods described here, and particularly in accordance with the processes described in detail with regard to the CPU 1606; or (iii) database(s) 1616 adapted to store information that may be utilized to store information required by the program. In some aspects, the database(s) includes or comprises a database storing experimental data, and published literature models.

The operating system 1612 and applications 1614 may be stored, for example, in a compressed, an uncompiled and an encrypted format, and may include or comprise computer program code. The instructions of the program may be read into a main memory of the processor from a computer-readable medium other than the data storage device, such as from the ROM 1604 or from the RAM 1602. While execution of sequences of instructions in the program causes the CPU 1606 to perform the process steps described herein, hard-wired circuitry may be used in place of, or in combination with, software instructions for implementation of the processes of the present invention. Thus, the systems and methods described are not limited to any specific combination of hardware and software.

Suitable computer program code may be provided for performing one or more functions in relation to modeling, scoring and aggregating as described herein. The program also may include or comprise program elements such as an operating system 1612, a database management system and “device drivers” that allow the processor to interface with computer peripheral devices (e.g., a video display, a keyboard, a computer mouse, etc.) via the input/output controller 1610.

The term “computer-readable medium” as used herein refers to any non-transitory medium that provides or participates in providing instructions to the processor of the computing device 1600 (or any other processor of a device described herein) for execution. Such a medium may take many forms, including but not limited to, non-volatile media and volatile media. Non-volatile media include or comprise, for example, optical, magnetic, or opto-magnetic disks, or integrated circuit memory, such as flash memory. Volatile media include or comprise dynamic random access memory (DRAM), which typically constitutes the main memory. Common forms of computer-readable media include or comprise, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, a RAM, a PROM, an EPROM or EEPROM (electronically erasable programmable read-only memory), a FLASH-EEPROM, any other memory chip or cartridge, or any other non-transitory medium from which a computer can read.

Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to the CPU 1606 (or any other processor of a device described herein) for execution. For example, the instructions may initially be borne on a magnetic disk of a remote computer (not shown). The remote computer can load the instructions into its dynamic memory and send the instructions over an Ethernet connection, cable line, or even telephone line using a modem. A communications device local to a computing device 1600 (e.g., a server) can receive the data on the respective communications line and place the data on a system bus for the processor. The system bus carries the data to main memory, from which the processor retrieves and executes the instructions. The instructions received by main memory may optionally be stored in memory either before or after execution by the processor. In addition, instructions may be received via a communication port as electrical, electromagnetic or optical signals, which are exemplary forms of wireless communications or data streams that carry various types of information. Further aspects and embodiments are set forth in the following passages:

1. A computerized method for quantifying the perturbation of a biological system in response to an agent, comprising receiving, at a first processor, a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes or comprises a plurality of biological entities, each biological entity interacting with at least one other of the biological entities; receiving, at a second processor, a set of control data corresponding to the biological system not exposed to the agent; providing, at a third processor, a computational casual network model that represents the biological system and includes or comprises: nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data; calculating, with a fourth processor, activity measures, for the nodes, representing a difference between the treatment data and the control data; calculating, with a fifth processor, weight values for the nodes, wherein at least one weight value is different from at least one other weight value; and generating, with a sixth processor, a score for the computational model representative of the perturbation of the biological system to the agent, wherein the score is based on the direction values, the weight values and the activity measures. 2. The computerized method of passage 1, further comprising normalizing the score based on the number of nodes in the respective computational model. 3. The computerized method of any of the above passages, wherein the weight values represent a confidence in at least one of the set of treatment data and control data. 4. The computerized method of any of the above passages, wherein the weight values include local false non-discovery rates. 5. The computerized method of passage 1, further comprising calculating, with a seventh processor, an approximate distribution of the activity measures over the node; calculating, with an eighth processor, an expected value of the approximate distribution; and generating, with a ninth processor, a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on expected value. 6. The computerized method of passage 5, wherein the approximate distribution is based on the activity measures. 7. The computerized method of any of passages 5-6, wherein calculating an expected value comprises performing a rectangular approximation. 8. The computerized method of passage 1, further comprising calculating, with a tenth processor, a positive activation score and a negative activation score based on the activity measures, the positive and negative activation scores representative of consistency and inconsistency, respectively, between the activity measures and the direction values; and generating, with an eleventh processor, a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on the positive and negative activation scores. 9. The computerized method of passage 8, wherein the score is based on local false non-discovery rates. 10. The computerized method of any of passages 8-9, wherein the activity measure is a fold-change value, and the fold-change value for each node includes a logarithm of the difference between the treatment data and the control data for the biological entity represented by the respective node. 11. The computerized method of any of the above passages, wherein the subset of the biological system includes at least one of cell proliferation mechanism, cellular stress mechanism, cell inflammation mechanism, and DNA repair mechanism. 12. The computerized method of any of the above passages, wherein the agent includes at least one of aerosol generated by heating tobacco, aerosol generated by combusting tobacco, tobacco smoke or cigarette smoke. 13. The computerized method of any of the above passages, wherein the agent includes a heterogeneous substance, including a molecule or an entity that is not present in or derived from the biological system. 14. The computerized method of any of the above passages, wherein the agent includes toxins, therapeutic compounds, stimulants, relaxants, natural products, manufactured products, and food substances. 15. The computerized method of any of the above passages, wherein the set of treatment data includes a plurality of sets of treatment data such each node includes a plurality of fold-change values defined by a first probability distribution and a plurality of weight values defined by a second probability distribution.

While implementations of the invention have been particularly shown and described with reference to specific examples, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced. 

1. A computerized method for quantifying the perturbation of a biological system in response to an agent, comprising receiving, at a first processor, a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes or comprises a plurality of biological entities, each biological entity interacting with at least one other of the biological entities; receiving, at a second processor, a set of control data corresponding to the biological system not exposed to the agent; providing, at a third processor, a computational causal network model that represents the biological system and includes or comprises: nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data; calculating, with a fourth processor, activity measures, for the nodes, representing a difference between the treatment data and the control data; calculating, with a fifth processor, weight values for the nodes, wherein at least one weight value is different from at least one other weight value; and generating, with a sixth processor, a score for the computational model representative of the perturbation of the biological system to the agent, wherein the score is based on the direction values, the weight values and the activity measures.
 2. The computerized method of claim 1, wherein the biological system is represented by at least one mechanism hypothesis.
 3. The computerized method of claim 1, wherein the biological system is represented by a plurality of computational causal network models or at least one computational causal network model comprising a plurality of mechanism hypotheses.
 4. The computerized method of claim 1, further comprising normalizing the score based on the number of measurable nodes in the respective computational model.
 5. The computerized method of claim 1, wherein the weight values represent a confidence in at least one of the set of treatment data and control data.
 6. The computerized method of claim 1, wherein the weight values include or comprise local false non-discovery rates.
 7. The computerized method of claim 1, further comprising calculating, with a seventh processor, an approximate distribution of the activity measures of nodes over a model or a mechanism hypotheses in a model; calculating, with an eighth processor, an expected value of activity measures with respect to the approximate distribution; and generating, with a ninth processor, a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on expected value.
 8. The computerized method of claim 7, wherein the approximate distribution is based on the activity measures.
 9. The computerized method of claim 7, wherein calculating an expected value comprises performing a rectangular approximation.
 10. The computerized method of claim 1, further comprising calculating, with a tenth processor, a positive activation metric and a negative activation metric based on the activity measures, the positive and negative activation metrics representative of consistency and inconsistency, respectively, between the activity measures and the direction values with respect to the model; and generating, with an eleventh processor, a score for each computational model representative of the perturbation of the subset of the biological system to the agent, wherein the score is based on the positive and negative activation scores.
 11. The computerized method of claim 1, wherein the positive activation metric, negative activation metric or both are based on local false non-discovery rates.
 12. The computerized method of claim 1, wherein the activity measure is a fold-change value, and the fold-change value for each node includes or comprises a logarithm of the difference between the treatment data and the control data for the biological entity represented by the respective node.
 13. The computerized method of claim 1, wherein the subset of the biological system includes or comprises at least one of cell proliferation mechanism, cellular stress mechanism, cell inflammation mechanism, and DNA repair mechanism.
 14. The computerized method of claim 1, wherein the agent includes or comprises at least one of aerosol generated by heating tobacco, aerosol generated by combusting tobacco, tobacco smoke or cigarette smoke.
 15. The computerized method of claim 1, wherein the agent includes or comprises a heterogeneous substance, including a molecule or an entity that is not present in or derived from the biological system.
 16. The computerized method of claim 1, wherein the agent includes or comprises toxins, therapeutic compounds, stimulants, relaxants, natural products, manufactured products, and food substances.
 17. The computerized method of claim 1, wherein the set of treatment data includes or comprises a plurality of sets of treatment data such that each measurable node includes or comprises a plurality of fold-change values defined by a first probability distribution and a plurality of weight values defined by a second probability distribution.
 18. The computerized method of claim 1, wherein the set of treatment data includes or comprises a plurality of sets of treatment data such that each measurable node includes or comprises a plurality of fold-change values and the corresponding weight values.
 19. The computerized method of claim 1, wherein the step of generating the score comprises a linear or a non-linear combination of the activity measures, the weight values, and the direction values; and a normalization of the combination by a scale factor.
 20. The computerized method of claim 19, wherein the combination is an arithmetic combination, and the scale factor is the square root of the number of biological entities for which measured data are received.
 21. The computerized method of claim 1, wherein the score is generated by a geometric perturbation index scoring technique, a probabilistic perturbation index scoring technique, or an expected perturbation index scoring technique.
 22. The computerized method of claim 1, further comprising determining a confidence interval for the score based on a parametric or non-parametric computational bootstrapping technique.
 23. A computer system for quantifying the perturbation of a biological system in response to an agent, the system comprising at least one processor configured or adapted to: receive a set of treatment data corresponding to a response of a biological system to an agent, wherein the biological system includes or comprises a plurality of biological entities, each biological entity interacting with at least one other of the biological entities; receive a set of control data corresponding to the biological system not exposed to the agent; provide a computational causal network model that represents the biological system and includes or comprises: nodes representing the biological entities, edges representing relationships between the biological entities, and direction values, for the nodes, representing the expected direction of change between the control data and the treatment data; calculate activity measures, for the nodes, representing a difference between the treatment data and the control data; calculate weight values for the nodes, wherein at least one weight value is different from at least one other weight value; and generate a score for the computational model representative of the perturbation of the biological system to the agent, wherein the score is based on the direction values, the weight values and the activity measures.
 24. (canceled)
 25. (canceled) 